Exhibit 4.1

NUMBER OF UNITS

CUSIP G1R59T124

SEE REVERSE FOR

CERTAIN DEFINITIONS

BHAIU

BHAV ACQUISITION CORP II

UNITS CONSISTING OF ONE CLASS A ORDINARY SHARE AND
ONE RIGHT TO RECEIVE ONE-FOURTH OF ONE CLASS A ORDINARY SHARE

_______________________________________________________________________________________________ is the owner of ___________________________________________________________________________________ Units.

Each Unit (“Unit”) consists of one (1) Class A Ordinary Share, par value $0.0001 per share (“Class A Ordinary Shares”), of BHAV Acquisition Corp II, a Cayman Islands exempted company (the “Company”), and one right (the “Rights”) to receive one-fourth (1/4) of one Class A Ordinary Share. Every four (4) Rights entitles the holder thereof to receive one Class A Ordinary Share upon the consummation of the Company’s initial completion of a merger, amalgamation, share exchange, asset acquisition, share purchase, recapitalization, reorganization or other similar business combination with one or more businesses (each a “Business Combination”). The Class A Ordinary Shares and Rights comprising the Units represented by this certificate will begin separate trading on [●], 2026, unless Maxim Group LLC elects to allow separate trading earlier, subject to the Company’s filing of a Current Report on Form 8-K with the Securities and Exchange Commission containing an audited balance sheet reflecting the Company’s receipt of the gross proceeds of its initial public offering and issuing a press release announcing when separate trading will begin. The terms of the Rights are governed by a Rights Agreement (the “Rights Agreement”), dated as of [●], 2026, between the Company and Continental Stock Transfer & Trust Company (the “Rights Agent” or “Transfer Agent”), as Rights Agent, and are subject to the terms and provisions contained therein, all of which terms and provisions the holder of this certificate consents to by acceptance hereof. Copies of the Rights Agreement are on file at the office of the Rights Agent at One State Street, 30th Floor, New York, New York 10004, and are available to any Rights holder on written request and without cost.

This certificate is not valid unless countersigned by the Transfer Agent and registered by the Registrar of the Company.

Each Unit may be mandatorily split by the Company in connection with the closing of a Business Combination.

Witness the facsimile seal of the Company and the facsimile signatures of its duly authorized officers.

This Unit Certificate shall be governed and construed in accordance with the internal laws of the State of New York, without regard to conflicts of laws principles thereof.

BHAV Acquisition Corp II

The Company will furnish without charge to each unitholder who so requests, a statement of the powers, designations, preferences and relative, participating, optional or other special rights of each class of shares or series thereof of the Company and the qualifications, limitations, or restrictions of such preferences and/or rights.

The following abbreviations, when used in the inscription on the face of this certificate, shall be construed as though they were written out in full according to applicable laws or regulations:

Additional Abbreviations may also be used though not in the above list.

For value received, ___________________________hereby sell(s), assign(s) and transfer(s) unto

(PLEASE PRINT OR TYPEWRITE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE(S))

Units

represented by the within Certificate, and do hereby irrevocably constitute and appoint

Attorney

to transfer the said Units on the books of the within named Company with full power of substitution in the premises.

Dated _____________________

Signature(s) Guaranteed:

_________________________________________________________________

THE SIGNATURE(S) SHOULD BE GUARANTEED BY AN ELIGIBLE
GUARANTOR INSTITUTION (BANKS, STOCKBROKERS, SAVINGS AND
LOAN ASSOCIATIONS AND CREDIT UNIONS WITH MEMBERSHIP IN

AN APPROVED SIGNATURE GUARANTEE MEDALLION PROGRAM,
PURSUANT TO S.E.C. RULE 17Ad-15).

In each case, as more fully described in the Company’s final prospectus dated [●], 2026, the holder(s) of this certificate shall be entitled to receive a pro rata portion of certain funds held in the trust account established in connection with its initial public offering only in the event that (i) the Company redeems the Class A Ordinary Shares sold in its initial public offering and liquidates because it does not consummate an initial business combination by [●], 2027, or such earlier date as the Company’s board of directors may approve, or by such later date approved by the Company’s shareholders in accordance with the Company’s amended and restated memorandum and articles of association, (ii) the Company redeems the Class A Ordinary Shares sold in its initial public offering in connection with a shareholder vote to amend the Company’s amended and restated memorandum and articles of association (A) to modify the substance or timing of the Company’s obligation to allow redemption in connection with the Company’s initial business combination or to redeem 100% of the Class A Ordinary Shares if it does not complete its initial business combination by [●], 2027, or such earlier date as the Company’s board of directors may approve, or by such later date approved by the Company’s shareholders in accordance with the Company’s amended and restated memorandum and articles of association, or (B) with respect to any other provision relating to the holder(s)’ rights or pre-initial business combination activity, or (iii) if the holder(s) seek(s) to redeem for cash his, her, its or their respective Class A Ordinary Shares in connection with a tender offer (or proxy solicitation, solely in the event the Company seeks shareholder approval of the proposed initial business combination) setting forth the details of a proposed initial business combination. In no other circumstances shall the holder(s) have any right or interest of any kind to or in the trust account.