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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsNonrecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Nonrecurring [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsNonrecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Nonrecurring [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueInputsValuationTechnique_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Valuation Techniques</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueInputsValuationTechnique_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Inputs Valuation Technique</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueInputsValuationTechnique_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Fair value inputs, valuation technique.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Recurring [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueMeasurementsRecurringMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Assets Measured at Fair Value on a Recurring Basis [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations of U.S. government-sponsored enterprises Mortgage-backed securities-residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">USGovernment Sponsored Enterprises Debt Securities Residential Mortgage Backed Securities Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_USGovernmentSponsoredEnterprisesDebtSecuritiesResidentialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">U.S. government-sponsored enterprises securities collateralized by residential real estate mortgage loans.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities available for sale:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Securities available-for-sale:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableforsaleAmortizedCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations of U.S. government agencies:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsFairValueDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Fair Value Disclosure [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsLiabilitiesAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsLiabilitiesAtFairValueNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Assets (Liabilities), at Fair Value, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueUnobservableInput_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unobservable Input</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueUnobservableInput_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Unobservable Input</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FairValueUnobservableInput_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unobservable Input of fair value.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other Comprehensive Income [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other comprehensive income, net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), before Tax</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossBeforeReclassificationsTaxAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Components of Other Comprehensive Income and the Related Income Tax Effects [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RestatementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revision of Prior Period [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Available-for-sale investments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment, after Tax</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RestatementDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revision of Prior Period [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FAIRVALUEDISCLOSURESScheduleofAssetsMeasuredatFairValueonaRecurringBasisDetailsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">FAIR VALUE DISCLOSURES - Schedule of Assets Measured at Fair Value on a Recurring Basis (Details) [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total securities available for sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2009/role/netLabel">Total investment securities, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/disclosureGuidance">Total securities available-for-sale, Fair value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment securities - available for sale, at fair value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Mortgage-backed securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfAssetsMeasuredAtFairValueOnARecurringBasisAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Assets Measured At Fair Value On ARecurring Basis [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Derivative liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Liability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mortgage-backed securities - commercial [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Mortgage-Backed Securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Amortized Cost, Mortgage-backed securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities Available-For-Sale, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollateralAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collateral Held [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResidentialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResidentialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Residential Real Estate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResidentialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Residential Real Estate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Mortgage-Backed Securities Available-for-Sale [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities Debt Securities and Mortgage Backed Securities Available-for-sale [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Commercial Real Estate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2009/role/netLabel">Commercial real estate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialRealEstateMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Real Estate [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByMeasurementBasisAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Measurement Basis [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Carrying Value [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CarryingReportedAmountFairValueDisclosureMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Reported Value Measurement [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EstimateOfFairValueFairValueDisclosureMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Estimate of Fair Value Measurement [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_SecuritiesAvailableForSaleFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities Available-For-Sale, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_SecuritiesAvailableForSaleFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Securities available-for-sale, fair value.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due within 1 year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due within 1 year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfMaturitiesDebtSecuritiesAndMortgageBackedSecuritiesHeldToMaturityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Mortgage-Backed Securities Held-to-Maturity [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities Available-For-Sale, Allowance for Credit Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities held-to-maturity:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityFairValueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Fair Value [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecurities_lbl" xlink:role="http://www.xbrl.org/2009/role/netLabel">Securities held-to-maturity, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment securities - held to maturity, at amortized cost (fair value of $60,924 and $61,160 at June 30, 2026 and September 30, 2025, respectively)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortized Cost, Mortgage backed securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesUnrealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total investment securities, Gross Unrealized Gains</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesUnrealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Unrealized Gain (Loss)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 1 but within 5 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total investment securities, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Fair Value, Mortgage-backed securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Amortized Cost, Total debt securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Fair Value, Total debt securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResidentialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mortgage backed securities - residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResidentialMortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mortgage-backed securities- residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByAssetClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_StandardPoorsBBBBBBRatingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Standard &amp; Poor's, BBB/BB/B Rating [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_StandardPoorsBBBBBBRatingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Standard Poors BBBBBBRating Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ExternalCreditRatingStandardPoorsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">External Credit Rating, Standard &amp; Poor's [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfAmortizedCostAndFairValuesOfSecuritiesClassifiedAsAvailableForSaleAndHeldtoMaturityTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Amortized Cost and Fair Values of Securities Classified as Available-for-Sale and Held-to-Maturity [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfAmortizedCostAndFairValuesOfSecuritiesClassifiedAsAvailableForSaleAndHeldtoMaturityTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Amortized Cost and Fair Values of Securities Classified as Available-For-Sale and Held-to-Maturity [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_MortgageBackedSecuritiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mortgage-backed securities:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_MortgageBackedSecuritiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mortgage Backed Securities Abstract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 5 but within 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CorporateSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Corporate securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CorporateSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Corporate Securities Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NonratedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-rated [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NonratedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonrated Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_StandardPoorsAAAAAARatingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Standard &amp; Poor's, AAA/AA/A Rating [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_StandardPoorsAAAAAARatingMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Standard Poors AAAAAARating Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CreditRatingStandardPoorsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Rating, Standard &amp; Poor's [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfAmortizedCostAndFairValuesOfSecuritiesHeldToMaturityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Amortized Cost and Fair Values of Securities Classified as Available-for-Sale and Held-to-Maturity [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Securities Available-For-Sale, Gross Unrealized Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_INVESTMENTSECURITIESScheduleofAmortizedCostandFairValuesofSecuritiesHeldtoMaturityDetailsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">INVESTMENT SECURITIES - Schedule of Amortized Cost and Fair Values of Securities Classified as Available-for-Sale and Held-to-Maturity [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_INVESTMENTSECURITIESScheduleofAmortizedCostandFairValuesofSecuritiesHeldtoMaturityDetailsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">INVESTMENT SECURITIES - Schedule of Amortized Cost and Fair Values of Securities Held to Maturity (Details) [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfUSGovernmentAgenciesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations of U.S. government agencies [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfUSGovernmentAgenciesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Obligations Of USGovernment Agencies Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InformationByCategoryOfDebtSecurityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Security Category [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PrivateLabelMortgagebackedSecuritiesResidentialMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Private label mortgage-backed securities residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PrivateLabelMortgagebackedSecuritiesResidentialMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Private Label Mortgagebacked Securities Residential Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities Available-For-Sale, Gross Unrealized Gains</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesGrossUnrealizedGain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Gain</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total securities held-to-maturity, Amortized cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total securities held-to-maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Current, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AmortizedCostTotalSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total securities available-for-sale, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AmortizedCostTotalSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amortized Cost Total Securities Available for sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AmortizedCostTotalSecuritiesAvailableForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of amortized cost, total securities available-for-sale.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Total securities held-to-maturity fair value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair value of investment securities - held to maturity (in Dollars)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2009/role/netLabel">Fair Value, Mortgage backed securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mortgage-Backed Securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MortgageBackedSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collateralized Mortgage-Backed Securities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 5 but within 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfUSGovernmentsponsoredEnterprisesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations of U.S. government-sponsored enterprises [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfUSGovernmentsponsoredEnterprisesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Obligations Of USGovernmentsponsored Enterprises Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfUnrealizedLossesOfAvailableForSaleSecuritiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Available-for-Sale Securities with Unrealized Losses [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_TwelveMonthsOrGreaterMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">12 Months or Greater [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_TwelveMonthsOrGreaterMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Twelve Months Or Greater Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_UNREALIZEDLOSSESONINVESTMENTSECURITIESAVAILABLEFORSALEScheduleofUnrealizedLossesofAvailableforSaleSecuritiesDetailsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">UNREALIZED LOSSES ON INVESTMENT SECURITIES AVAILABLE-FOR-SALE - Schedule of Unrealized Losses of Available-for-Sale Securities (Details) [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableforsaleAllowanceForCreditLossLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Schedule of Unrealized Losses of Available-for-Sale Securities [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableforsaleAllowanceForCreditLossLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Unrealized Losses of Available-for-Sale Securities [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquitySecuritiesByInvestmentObjectiveAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Objective [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquitySecuritiesInvestmentObjectiveMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Objective [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentOwnedAtFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Owned, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Gain (Loss) on Investments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial relationships amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Relationships Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of commercial relationships.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CriticizedRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Criticized relationships amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CriticizedRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Criticized Relationships Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CriticizedRelationshipsAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of criticized relationships.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LOANSRECEIVABLENETANDRELATEDALLOWANCEFORCREDITLOSSESDetailsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR CREDIT LOSSES (Details) [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PercentageOfLoanReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of loan receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PercentageOfLoanReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of Loan Receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PercentageOfLoanReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of loan receivable.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loans Receivable, Net and Related Allowance for Credit Losses [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsNotesAndLoansReceivableLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Loans Receivable [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction and land</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction in Progress, Gross</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction and Land [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionLoansMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction Loans [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRecordedInvestmentByClassOfFinancingReceivableAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Financing Receivable [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 5 but within 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterFiveThroughTenYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 5 through 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 1 but within 5 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year One through Five</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Mortgage-Backed Securities Held-to-Maturity [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfHeldToMaturitySecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Maturities Debt Securities and Mortgage Backed Securities Held to Maturity [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due within 1 year</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DoubtfulMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Doubtful [Member]</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedFiveOrMoreYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Originated, More than Five Years before Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loans Amortized Cost Basis by Origination Fiscal Year 2022/ 2021</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedFourYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Five, Originated, Four Years before Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loans Amortized Cost Basis by Origination Fiscal Year 2026/ 2025</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedInCurrentFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year One, Originated, Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loans Amortized Cost Basis by Origination Fiscal Year 2025/ 2024</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedInFiscalYearBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Two, Originated, Fiscal Year before Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedMoreThanFiveYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Originated, More than Five Years before Current Fiscal Year, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loans Amortized Cost Basis by Origination Fiscal Year 2023/ 2022</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedThreeYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Four, Originated, Three Years before Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Term Loans Amortized Cost Basis by Origination Fiscal Year 2024/ 2023</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableOriginatedTwoYearsBeforeLatestFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Three, Originated, Two Years before Current Fiscal Year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRecordedInvestmentClassOfFinancingReceivableDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Class of Financing Receivable [Domain]</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoan_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Revolving Loans Converted to Term</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoan_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Revolving, Converted to Term Loan</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoanWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingConvertedToTermLoanWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Revolving, Converted to Term Loan, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableRevolvingWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Revolving, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearFiveOriginatedFourYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Five, Originated, Four Years before Current Fiscal Year, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearFourOriginatedThreeYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Four, Originated, Three Years before Current Fiscal Year, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearOneOriginatedCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearOneOriginatedCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year One, Originated, Current Fiscal Year, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current period gross charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableYearThreeOriginatedTwoYearsBeforeCurrentFiscalYearWriteoff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Year Three, Originated, Two Years before Current Fiscal Year, Writeoff</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableTransferToHeldForInvestmentAllowanceForCreditLossExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recorded investment</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableTransferToHeldForInvestmentAllowanceForCreditLossExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Transfer to Held-for-Investment, Allowance for Credit Loss, Expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFinancingReceivablesPastDueTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Past Due [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR CREDIT LOSSES</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansNotesTradeAndOtherReceivablesDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans, Notes, Trade and Other Receivables Disclosure [Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndEquityInstrumentsCashAndCashEquivalentsUnrealizedAndRealizedGainsLossesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">UNREALIZED LOSSES ON INVESTMENT SECURITIES AVAILABLE-FOR-SALE</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesUnrealizedGainLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Losses on Investment Securities Available-for-Sale [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">INVESTMENT SECURITIES</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments in Debt and Marketable Equity Securities (and Certain Trading Assets) Disclosure [Text Block]</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ConstructionAndLandMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Construction and land [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ConstructionAndLandMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction and Land [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ConstructionAndLandMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction And Land Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HomeLoansAndLinesOfCreditMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Home Loans and Lines of Credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_OneToFourFamilyResidentialMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One-to-four family residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_OneToFourFamilyResidentialMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">One to four family residential [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allowance for credit losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Allowance of individually evaluated loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesIndividuallyEvaluatedForImpairment1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss, Individually Evaluated</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Individually Evaluated Loans [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Allowance for Loan Losses by Loan Category [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableIndividuallyEvaluatedForCreditLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Individually Evaluated Loans [Abstarct]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableIndividuallyEvaluatedForCreditLossAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Individually Evaluated for Credit Loss [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unpaid principal balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableIndividuallyEvaluatedForImpairment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Individually Evaluated for Credit Loss, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfOtherFinancialAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net gains on OREO</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnDispositionOfOtherFinancialAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Disposition of Other Financial Assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfLoansAndLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Gains on SBA loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSaleOfLoansAndLeases_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gain (Loss) on Sale of Loans and Leases</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Income before income tax expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesExtraordinaryItemsNoncontrollingInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income tax expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeTaxExpenseBenefit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Tax Expense (Benefit)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total comprehensive income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ComprehensiveIncomeNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized gain on securities available for sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossAvailableForSaleSecuritiesAdjustmentNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">OCI, Debt Securities, Available-for-Sale, Gain (Loss), after Adjustment and Tax</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other comprehensive income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Other comprehensive income (loss)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTaxAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTaxAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Tax [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Deferred income tax effect</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Tax, Portion Attributable to Parent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_TreasuryStock1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Treasury Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_TreasuryStock1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Treasury Stock1 Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_UnearnedEsopSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unearned ESOP Shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_UnearnedEsopSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unearned Esop Shares Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_UnearnedEsopSharesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Unearned ESOP Shares Member.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-In Capital</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationEmployeeStockPurchaseProgramRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ESOP shares allocated</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationEmployeeStockPurchaseProgramRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, ESPP, Increase for Cost Recognition</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalShareBasedCompensationStockOptionsRequisiteServicePeriodRecognition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Option, Increase for Cost Recognition</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Dividends paid on common stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DividendsCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Dividends, Common Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained Earnings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance (in Shares)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance (in Shares)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Shares, Outstanding</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementEquityComponentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Components [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Treasury stock used for exercised stock options (in Shares)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Restricted Stock Award, Gross</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Treasury stock used for exercised stock options</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of treasury stock (in Shares)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockRepurchasedDuringPeriodShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Repurchased During Period, Shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockValueAcquiredCostMethod_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of treasury stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockValueAcquiredCostMethod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockDividendsPerShareCashPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Dividends paid</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockDividendsPerShareCashPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Dividends, Per Share, Cash Paid</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CashPaidAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash paid for</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CashPaidAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash paid [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ChangeInFairValueOfSwapAssetliability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in fair value of swap asset/liability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ChangeInFairValueOfSwapAssetliability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change In Fair Value Of Swap Assetliability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ChangeInFairValueOfSwapAssetliability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in fair value of swap asset/liability.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DecreaseInOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">(Increase) decrease in other assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DecreaseInOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Decrease In Other Assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DecreaseInOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of decrease in other assets.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_IncreaseInSurrenderValueBankOwnedLifeInsurance_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Income on bank owned life insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_IncreaseInSurrenderValueBankOwnedLifeInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase In Surrender Value Bank Owned Life Insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_IncreaseInSurrenderValueBankOwnedLifeInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The increase (decrease) during the reporting period in surrender value of bank owned life insurance.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_InitialRecognitionOfLeaseLiabilityAndRightofuseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Initial recognition of lease liability and right-of-use asset</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_InitialRecognitionOfLeaseLiabilityAndRightofuseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Initial recognition of lease liability and right-of-use asset.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NetIncreaseInEscrowedFunds_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net increase in escrowed funds</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NetIncreaseInEscrowedFunds_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Increase In Escrowed Funds</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NoncashOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash operating activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NoncashOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non-cash operating activities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromMaturitiesOfInvestmentSecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Proceeds from maturities of investment securities held-to-maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromMaturitiesOfInvestmentSecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from maturities of investment securities held-to-maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromMaturitiesOfInvestmentSecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from maturities of investment securities held-to-maturity.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromSalesOfLoansReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the sales of SBA loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromSalesOfLoansReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds From Sales Of Loans Receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProceedsFromSalesOfLoansReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Proceeds from the sales of loans receivable.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProvisionForLossOnOtherRealEstateOwned_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for loss on other real estate owned</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProvisionForLossOnOtherRealEstateOwned_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Provision For Loss On Other Real Estate Owned</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ProvisionForLossOnOtherRealEstateOwned_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of provision for loss on other real estate owned.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PurchaseTreasuryStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchase of treasury stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PurchaseTreasuryStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Purchase Treasury Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PurchaseTreasuryStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of cash inflow (outflow) from purchase of treasury stock.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Discount on investment securities, net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Loss (gain) on the sales of other real estate owned</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainsLossesOnSalesOfInvestmentRealEstate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Gains (Losses) on Sales of Investment Real Estate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Preferred stock: $.01 Par Value, 500,000 shares authorized; at June 30, 2026 and September 30, 2025, none issued</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PreferredStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Preferred Stock, Value, Issued</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Premises and equipment, net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant and Equipment, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retained earnings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfFinancialPositionAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Financial Position [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net interest and dividend income after provision (recovery) for credit losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseAfterProvisionForLoanLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income (Expense), after Provision for Loan Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net interest and dividend income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income (Expense), Operating</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeSecuritiesTaxable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Taxable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeSecuritiesTaxable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Securities, Operating, Taxable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeSecuritiesTaxExempt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Tax-exempt</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeSecuritiesTaxExempt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Securities, Operating, Tax Exempt</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Compensation and employee benefits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LaborAndRelatedExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Labor and Related Expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoninterestExpenseDirectorsFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Director fees and benefits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NoninterestExpenseDirectorsFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Director Fee</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Total other expenses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonoperating Income (Expense)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NonoperatingIncomeExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nonoperating Income (Expense) [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OccupancyNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Occupancy expenses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OccupancyNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Occupancy, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other expenses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Expenses [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossCurrent_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Allowance for credit losses-loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAllowanceForCreditLossCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Allowance for Credit Loss, Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationEquity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unearned Employee Stock Ownership Plan shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCompensationEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Compensation Equity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Deposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Deposits_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Deposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FederalHomeLoanBankStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal Home Loan Bank of New York stock, at cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FederalHomeLoanBankStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Federal Home Loan Bank Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestBearingDepositsInBanks_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest earning deposits with banks</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestBearingDepositsInBanks_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest-Bearing Deposits in Banks and Other Financial Institutions</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued interest payable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPayableCurrentAndNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Payable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities and stockholders' equity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value (in Dollars per share)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Treasury stock, shares at cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockCommonShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Treasury Stock, Common, Shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FederalHomeLoanBankOfNewYorkStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal Home Loan Bank of New York stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FederalHomeLoanBankOfNewYorkStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Federal Home Loan Bank Of New York Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FederalHomeLoanBankOfNewYorkStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Dividend income from federal home loan bank investment.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_InterestRateSwapFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest rate swap fees</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_InterestRateSwapFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represents the amount of interest rate swap fees classified as income.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RecoveryForCreditLossesunfundedCommitments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision (recovery) for credit losses- unfunded commitments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RecoveryForCreditLossesunfundedCommitments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Recovery For Credit Lossesunfunded Commitments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RecoveryForCreditLossesunfundedCommitments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The amount of recovery for credit losses-unfunded commitments.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Operating and Nonoperating [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseBorrowings_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseBorrowings_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Borrowings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseOperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total interest expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestExpenseOperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Expense, Operating</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FederalDepositInsuranceCorporationPremiumExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">FDIC deposit insurance premiums</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FederalDepositInsuranceCorporationPremiumExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Federal Deposit Insurance Corporation Premium Expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LOANSRECEIVABLENETANDRELATEDALLOWANCEFORCREDITLOSSESScheduleofLoanPortfolioDetailsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">LOANS RECEIVABLE, NET AND RELATED ALLOWANCE FOR CREDIT LOSSES - Schedule of Loan Portfolio (Details) [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Home Equity Lines of Credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Home equity loans and lines of credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Home Equity Loan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForOtherLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision (credit)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForOtherLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Provision for Other Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFinancingReceivableAllowanceForCreditLossesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnallocatedFinancingReceivablesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unallocated [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnallocatedFinancingReceivablesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unallocated Financing Receivables [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DEPOSITSDetailsTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">DEPOSITS (Details) [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FDICInsurancBankDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">FDIC insurance limit on bank deposit accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FDICInsurancBankDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">FDICInsuranc Bank Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FDICInsurancBankDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The current FDIC insurance limit on bank deposit accounts.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NationalDepositListingService_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">National deposit listing service</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NationalDepositListingService_lbl" xlink:role="http://www.xbrl.org/2003/role/label">National Deposit Listing Service</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NationalDepositListingService_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of national deposit listing service.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFDICInsuredAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Federal deposit insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashFDICInsuredAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, FDIC Insured Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CertificatesOfDepositAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Brokered certificates of deposit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CertificatesOfDepositAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certificates of Deposit, at Carrying Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositLiabilityLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsByTypeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PledgingPurposeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pledging Purpose [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PledgingPurposeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Pledging Purpose [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Certificates of deposit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certificates Of Deposit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDeposit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of deposits that cannot be withdrawn before a set date without penalty or for which notice of withdrawal is required. The deposits include certificates of deposits and open accounts.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RetirementDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Retirement certificates</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RetirementDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retirement Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RetirementDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of deposits that cannot be withdrawn before a set date without penalty or for which notice of withdrawal is required. The deposits include individual retirement accounts.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DemandDepositAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Demand accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DemandDepositAccounts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Demand Deposit Accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Deposits by Type of Account [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsMoneyMarketDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money market accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsMoneyMarketDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits, Money Market Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsNegotiableOrderOfWithdrawalNOW_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">NOW accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsNegotiableOrderOfWithdrawalNOW_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits, Negotiable Order of Withdrawal (NOW)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Loans Receivable, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accounts, Notes, Loans and Financing Receivable [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Available-for-Sale Securities with Unrealized Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized Gain (Loss) on Investments [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfIndividuallyEvaluatedLoansTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Individually Evaluated Loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfIndividuallyEvaluatedLoansTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Individually Evaluated Loans [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfIndividuallyEvaluatedLoansTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represents the entire table disclosure for the individually evaluated loans.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Allowance for Credit Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllowanceForCreditLossesOnFinancingReceivablesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfInterestBearingDepositsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Deposits by Type of Account</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfInterestBearingDepositsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Interest Bearing Deposits Table Text Block</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfInterestBearingDepositsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Tabular disclosure of composition of entities interest bearing deposits.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PriceRiskFairValueHedgeDerivativeAtFairValueNetAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments With Off-Balance Sheet Risk [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Information Regarding Derivatives</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfDerivativeInstrumentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Derivative Instruments [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Financial Instruments with Off-Balance-Sheet Risk</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfFairValueOffBalanceSheetRisksTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Fair Value, off-Balance-Sheet Risks [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Options and restricted shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Restricted shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsNonvestedNumberOfShares_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Nonvested, Number of Shares</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FAIRVALUEDISCLOSURESScheduleOfQuantitativeInformationAboutAssetsMeasuredAtFairValueOnANonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">FAIR VALUE DISCLOSURES - Schedule of Quantitative Information about Assets Measured at Fair Value on a Non-recurring Basis [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FAIRVALUEDISCLOSURESScheduleOfFairValueOnANonRecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">FAIR VALUE DISCLOSURES - Schedule of Fair Value on a Non-Recurring Basis [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FAIRVALUEDISCLOSURESScheduleOfFairValueOnANonRecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">FAIR VALUE DISCLOSURES - Schedule of Fair Value on a Non Recurring Basis [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total Liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Fair Value Disclosure</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Corporate securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MarketableSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marketable Securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AvailableForSaleHeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total investment securities, Gross Unrealized Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AvailableForSaleHeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Available For Sale Heldto Maturity Debt Securities Gross Unrealized Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AvailableForSaleHeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gross unrealized losses.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationByAssetClassDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset Class [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xlink:role="http://fasb.org/us-gaap/role/label/axisDefault">Portion at Fair Value Measurement [Member] [Default]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PortionAtFairValueFairValueDisclosureMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Portion at Fair Value Measurement [Member] [Default]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfQuantitativeInformationAboutAssetsMeasuredAtFairValueOnANonRecurringBasisAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Quantitative Information about Assets Measured at Fair Value on a Non-recurring Basis [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt, Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Company&#8217;s Bank Owned Life Insurance is not a Marketable Asset and May Generally Only be Redeemed with the Insurance Company [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueBalanceSheetGroupingFinancialStatementCaptionsLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of the Carrying Amount, Fair Value, and Placement in the Fair Value Hierarchy [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial instruments - liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherLiabilitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Liabilities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsHeldInTrust_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment securities held to maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsHeldInTrust_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Asset, Held-in-Trust</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByBalanceSheetGroupingTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, by Balance Sheet Grouping [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CollateralDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collateral Held [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfStateAndPoliticalSubdivisionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Obligations of state and political subdivisions	[Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfStateAndPoliticalSubdivisionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Obligations Of State And Political Subdivisions Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ObligationsOfStateAndPoliticalSubdivisionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Obligations of state and political subdivisions [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RangeWeightedAverage_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Range (Weighted Average)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RangeWeightedAverage_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Range Weighted Average</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_RangeWeightedAverage_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Range (Weighted Average).</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Quantitative Information about Assets Measured at Fair Value on a Non-recurring Basis [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherInvestmentsAndSecuritiesAtCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherInvestmentsAndSecuritiesAtCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Investments and Securities, at Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_SecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Securities held-to-maturity, Fair value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_SecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Securities held-to-maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_SecuritiesHeldtomaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of securities held-to-maturity.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherRealEstate_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Fair Value Estimate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherRealEstate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other real estate owned ("OREO")</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherRealEstate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Real Estate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesTransferredSecurityUnrealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities held-to-maturity, Gross Unrealized Gains</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesTransferredSecurityUnrealizedGainLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Transfer, Unrealized Gain (Loss)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 5 but within 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_MortgageBackedSecuritiesAbstract0_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Mortgage backed securities:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_MortgageBackedSecuritiesAbstract0_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mortgage Backed Securities Abstract0</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfTheCarryingAmountFairValueAndPlacementInTheFairValueHierarchyAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Company&#8217;s Bank Owned Life Insurance is not a Marketable Asset and May Generally Only be Redeemed with the Insurance Company [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansReceivableFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loan receivable net allowance for credit losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansReceivableFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable, Fair Value Disclosure</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDepositIncludingRetirementCertificates_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Certificates of deposit including retirement certificates</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDepositIncludingRetirementCertificates_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certificates Of Deposit Including Retirement Certificates</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CertificatesOfDepositIncludingRetirementCertificates_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Certificates of deposit including retirement certificates.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financial instruments - assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Securities held-to-maturity, Gross Unrealized Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Heldto Maturity Debt Securities Gross Unrealized Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HeldtoMaturityDebtSecuritiesGrossUnrealizedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Gross unrealized losses.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfMaturitiesDebtSecuritiesAndMortgageBackedSecuritiesAvailableForSaleAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Mortgage-Backed Securities Available-for-Sale [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 1 but within 5 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_InformationByCategoryOfDebtSecurityDomainDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">InformationByCategoryOfDebtSecurityDomain [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total investment securities, Amortized Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale and Held-to-Maturity, after Allowance for Credit Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Securities held-to-maturity, Allowance for Credit Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total investment securities, Allowance for Credit Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAndHeldToMaturityAmortizedCostAfterAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale and Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value, Due after 1 but within 5 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Fair Value, Maturity, Allocated and Single Maturity Date, after Year One Through Five</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Amortized Cost, Total debt securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due after 10 years</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesAfterTenYearsNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, after Year 10</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LessThan12MonthsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Less Than 12 Months [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LessThan12MonthsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Less Than12 Months Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NumberOfSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NumberOfSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NumberOfSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">The number of securities.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Off balance sheet commitments</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherCommitment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Commitment, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AdditionalProvisions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional provisions</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_AdditionalProvisions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Additional provisions.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NetLoanChargeOff_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loan charge-off</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NetLoanChargeOff_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Loan Charge-Off</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_NetLoanChargeOff_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of net loan charge-off.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Maturity, without Single Maturity Date, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithoutSingleMaturityDateNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, without Single Maturity Date</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Allowance for credit losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesPeriodIncreaseDecrease_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss, Period Increase (Decrease)</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Home Equity Line of Credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Home Equity Loans and Lines of Credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HomeEquityMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Home Equity Line of Credit [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Loans amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LoansPayable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Payable, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MortgageLoansInProcessOfForeclosureAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Residential loan in process of foreclosure</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MortgageLoansInProcessOfForeclosureAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Mortgage Loans in Process of Foreclosure, Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ReceivablesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable, Net and Related Allowance for Credit Losses [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial business</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Business</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of commercial business.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FinancingReceivableOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FinancingReceivableOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable Other Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_FinancingReceivableOtherMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represents details pertaining to other financing receivable.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HomeEquityLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Home equity loans and lines of credit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HomeEquityLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Home Equity Lines Of Credit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_HomeEquityLinesOfCredit_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of home equity lines of credit.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansAndLeasesReceivableDeferredCost_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Net deferred loan fees</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansAndLeasesReceivableDeferredCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans And Leases Receivable Deferred Cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansAndLeasesReceivableDeferredCost_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of deferred costs incurred to originate loans and leases from face amounts of acquired loans.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableGrossCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total loans receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableGrossCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable Gross Carrying Amount</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableGrossCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount before allowance of loans and leases held in portfolio, including but not limited to, commercial and consumer loans. Includes deferred interest and fees, undisbursed portion of loan balance, unamortized costs and premiums and discounts from face amounts. Excludes loans and leases covered under loss sharing agreements.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_OnetoFourfamilyResidential_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">One-to-four family residential</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_OnetoFourfamilyResidential_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Oneto Fourfamily Residential</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_OnetoFourfamilyResidential_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of family residential.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfLoansReceivableAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Loans Receivable Abstract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Business [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Loan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialPaperAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial real estate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommercialPaperAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commercial Paper, at Carrying Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amortized Cost, Due within 1 year</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesWithinOneYearNetCarryingAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Amortized Cost, after Allowance for Credit Loss, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfHeldToMaturitySecuritiesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Fair Value, Total debt securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_HeldToMaturitySecuritiesDebtMaturitiesSingleMaturityDateFairValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Held-to-Maturity, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">FINANCIAL INSTRUMENTS WITH OFF-BALANCE SHEET RISK</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments Disclosure [Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositLiabilitiesDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">DEPOSITS</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositLiabilitiesDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposit Liabilities Disclosures [Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivables30To59DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">30-59 Days Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivables30To59DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Asset, 30 to 59 Days Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivables60To89DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">60-89 Days Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivables60To89DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Asset, 60 to 89 Days Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">90 Days + Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivablesEqualToGreaterThan90DaysPastDueMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Asset, Equal to or Greater than 90 Days Past Due [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivablesPeriodPastDueAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Asset, Aging [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivablesPeriodPastDueDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Asset, Aging [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_EscrowedFunds_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Escrowed funds</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_EscrowedFunds_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Escrowed Funds</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndOtherAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable and other liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndOtherAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Other Accrued Liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInvestmentIncomeReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued interest receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedInvestmentIncomeReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Investment Income Receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated other comprehensive loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapital_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BankOwnedLifeInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Bank owned life insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BankOwnedLifeInsurance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Bank Owned Life Insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total cash and cash equivalents</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAtCarryingValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents, at Carrying Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermAccountsNotesAndLoansReceivableNetNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Loans receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermAccountsNotesAndLoansReceivableNetNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total loans receivable, net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermAccountsNotesAndLoansReceivableNetNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts and Financing Receivable, after Allowance for Credit Loss, Noncurrent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Borrowings</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Term Debt</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfLoanPortfolioAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Loan Portfolio Abstract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CreditFacilityAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Credit Facility [Axis]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromLifeInsurancePolicies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Redemption of bank owned life insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromLifeInsurancePolicies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Life Insurance Policy</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from long-term advances</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfLongTermDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Long-Term Debt</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchases of premises and equipment, net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireLoansReceivable_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Net increase in loans receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireLoansReceivable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Loans Receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireHeldToMaturitySecurities_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchases of investment securities held-to-maturity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireHeldToMaturitySecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Held-to-Maturity Securities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireFederalHomeLoanBankStock_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchase of Federal Home Loan Bank stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireFederalHomeLoanBankStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Federal Home Loan Bank Stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Purchases of investment securities available-for-sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquireAvailableForSaleSecuritiesDebt_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Debt Securities, Available-for-Sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Dividends paid on common stock</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsOfDebtIssuanceCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments of Debt Issuance Costs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherRealEstatePartnerships_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Proceeds from the sale of other real estate owned</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForProceedsFromOtherRealEstatePartnerships_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for (Proceeds from) Other Real Estate Partnerships</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by operating activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Operating Activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investing activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Investing Activities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in investing activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation, Total</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Financing activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Financing Activities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by financing activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Cash Provided by (Used in) Financing Activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestPaidNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Paid, Excluding Capitalized Interest, Operating Activities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase (decrease) in accounts payable and other liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOtherAccountsPayableAndAccruedLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Other Accounts Payable and Accrued Liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DirectFinancingLeaseNetInvestmentInLeasePastDueLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of the Loan Portfolio by Analyzing the Age [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsumerLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Business [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConsumerLoanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consumer Loan [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfTheLoanPortfolioByAnalyzingTheAgeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of The Loan Portfolio By Analyzing The Age Abstract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Past Due</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable Past Dues</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDues_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Represent the amount of loans receivable past due.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Total Loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable Past Due</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivablePastDue_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loans receivable, past due.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Loans Receivable Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_LoansReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Loans receivable, current.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Decrease (increase) in accrued interest receivable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccruedInterestReceivableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Accrued Interest Receivable, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAssetsHeldForSale_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Originations of SBA loans held for sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAssetsHeldForSale_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Asset, Held-for-Sale</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net increase in deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInterestPayableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase (decrease) in accrued interest payable</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInInterestPayableNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Interest Payable, Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_Chargeoffs_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Charge-offs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_Chargeoffs_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Chargeoffs</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_Chargeoffs_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Amount of charge-off means a lender or creditor has written the account off as a loss, and the account is closed to future charges. It may be sold to a debt buyer or transferred to a collection agency. You are still legally obligated to pay the debt.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Reconciling items that impact the rate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EffectiveIncomeTaxRateReconciliationOtherReconcilingItemsPercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Effective Income Tax Rate Reconciliation, Other Reconciling Items, Percent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">LEASES</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Leases [Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Balance Sheet Information Related to our Leases</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Table Text Block]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PercentageOfLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage of lease liability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_PercentageOfLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of lease liability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rental expenses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsForRent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments for Rent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use asset</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average discount rate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinanceLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Finance Lease, Weighted Average Discount Rate, Percent</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Balance Sheet Information Related to our Leases [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseCostAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lease, Cost [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease right-of-use asset</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherReceivables_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Receivables</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccountsNotesLoansAndFinancingReceivableTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts and Financing Receivables [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_CommercialBusinessMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commercial Business [Member]</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Line Items]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentInformationTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Information [Table]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressPostalZipCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Postal Zip Code</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFileNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity File Number</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityFilerCategory_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Filer Category</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_LocalPhoneNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Local Phone Number</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfAllowanceForLoanLossesByLoanCategoryAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of Allowance For Loan Losses By Loan Category Abstract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Balance-Ending balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Balance - Beginning balance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Recoveries</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancingReceivableAllowanceForCreditLossesRecovery_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financing Receivable, Allowance for Credit Loss, Recovery</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares issued</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Issued</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' equity</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockValue_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Treasury stock: 640,622 and 617,797 shares at June 30, 2026 and September 30, 2025, respectively, at cost</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TreasuryStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Treasury Stock, Value</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ServiceChargeIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Service charges</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ServiceChargeIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Service Charge Income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ServiceChargeIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Income on service charges for the period.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BankOwnedLifeInsuranceIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Income on bank owned life insurance</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BankOwnedLifeInsuranceIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Bank Owned Life Insurance Income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marketing and business development</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BusinessDevelopment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Business Development</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other operating income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Operating Income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total other income</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherOperatingIncomeExpenseNet_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Operating Income (Expense), Net</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfessionalFees_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Professional fees</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfessionalFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Professional Fees</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForOtherCreditLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Provision for credit losses- loans</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProvisionForOtherCreditLosses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Provision for Other Credit Losses</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Initial term lease</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Term of Contract</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease, option to extend</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Option to Extend</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Adjustments to reconcile net income to net cash provided by operating activities:</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustments to Reconcile Net Income (Loss) to Cash Provided by (Used in) Operating Activities [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents, end of period</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents, beginning of period</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net increase in cash and cash equivalents</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseExcludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Period Increase (Decrease), Excluding Exchange Rate Effect</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxesAndTaxCredits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred income tax benefit</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredIncomeTaxesAndTaxCredits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Income Taxes and Tax Credits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ESOP compensation expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeStockOwnershipPlanESOPCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee Stock Ownership Plan (ESOP), Compensation Expense</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GainLossOnSalesOfLoansNet_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Gains on sale of SBA loans</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsSavingsDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Savings accounts</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DepositsSavingsDeposits_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deposits, Savings Deposits</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ClassifiedInOtherAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Classified in Other Assets [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ClassifiedInOtherAssetsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Classified In Other Assets Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ClassifiedInOtherLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Classified in Other Liabilities [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ClassifiedInOtherLiabilitiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Classified In Other Liabilities Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DerivativesWeightedAverageVariableRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Variable Rate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DerivativesWeightedAverageVariableRate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivatives Weighted Average Variable Rate</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_DerivativesWeightedAverageVariableRate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Weighted Average Variable Rate.</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ScheduleOfInformationRegardingDerivativesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Information Regarding Derivatives [Abstract]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ThirdPartyInterestRateSwapsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">3rd Party Interest Rate swaps [Member]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="mgyr_ThirdPartyInterestRateSwapsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Third Party Interest Rate Swaps Member</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Classified in Other Assets:</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAverageFixedInterestRate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted Average Fixed Rate</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeAverageRemainingMaturity1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Average Maturity (Years)</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeContractTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Contract [Domain]</link:label>
    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeFairValueOfDerivativeNet_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeInstrumentRiskAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative Instrument [Axis]</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeNotionalAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative, Notional Amount</link:label>
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    <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DerivativeTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Derivative [Table]</link:label>
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