Exhibit 4.1

Execution Version

THIRD SUPPLEMENTAL INDENTURE

This THIRD SUPPLEMENTAL INDENTURE, dated as of March 2, 2026 (this “Supplemental Indenture”) is among Transocean International Limited (f/k/a Transocean Inc.), a Bermuda exempted company limited by shares (the “Company”), GlobalSantaFe Drilling Mexico, S. De R.L. De C.V., a company organized under the laws of Mexico (the “Additional Guarantor”), which is a subsidiary of Transocean Ltd., a limited liability company organized under the laws of Switzerland, each of the other existing Note Parties (as defined in the Indenture referred to below) and Truist Bank, as Trustee and Collateral Agent.

RECITALS

WHEREAS, the Company, the other Note Parties, the Trustee and the Collateral Agent entered into an Indenture, dated as of January 31, 2023 (as heretofore amended, supplemented or otherwise modified, the “Indenture”), providing for the issuance of the Company’s 8.75% Senior Secured Notes due 2030 (the “Securities”);

WHEREAS, the Indenture provides that under certain circumstances the Additional Guarantor shall execute and deliver to the Trustee and the Collateral Agent a supplemental indenture pursuant to which the Additional Guarantor shall become a Guarantor (as defined in the Indenture); and

WHEREAS, Section 10.01(d) of the Indenture provides that the Company, the other Note Parties, the Trustee and the Collateral Agent may amend or supplement the Indenture in order to add any additional Guarantor with respect to the Securities, without the consent of the Holders of the Securities;

NOW, THEREFORE, to comply with the provisions of the Indenture and in consideration of the above premises, the Company, the Additional Guarantor, the other Note Parties, the Trustee and the Collateral Agent covenant and agree for the equal and proportionate benefit of the respective Holders of the Securities as follows:

Section 1. Capitalized Terms. Capitalized terms used herein without definition shall have the meanings ascribed to them in the Indenture.

Section 2. Relation to Indenture. This Supplemental Indenture is supplemental to the Indenture and does and shall be deemed to form a part of, and shall be construed in connection with and as part of, the Indenture for any and all purposes.

Section 3. Effectiveness of Supplemental Indenture. This Supplemental Indenture shall become effective immediately upon its execution and delivery by each of the Company, the Additional Guarantor, the other Note Parties, the Trustee and the Collateral Agent.

Section 4. Agreement to Guarantee. The Additional Guarantor hereby agrees to, and by its execution of this Supplemental Indenture hereby does, become a party to the Indenture as a Guarantor and as such shall have all of the rights and is bound by the provisions of the Indenture applicable to Guarantors to the extent provided for and subject to the limitations therein, including Article 11 thereof.  The Additional Guarantor hereby unconditionally and irrevocably guarantees, jointly and severally, on a senior basis to each Holder and to the Trustee and the Collateral Agent and their successors and assigns (a) the full and punctual payment of principal of and interest on the Securities when due, whether at maturity, by acceleration, by redemption or otherwise, and all other monetary obligations of the Company under the Indenture with respect to the Securities and (b) the full and punctual performance within applicable grace periods of all other obligations of the Company under the Indenture with respect to the Securities.

Section 5. Ratification of Obligations. Except as specifically modified herein, the Indenture and the Securities are in all respects ratified and confirmed (mutatis mutandis) and shall remain in full force and effect in accordance with their terms.

Section 6. The Trustee and Collateral Agent. Except as otherwise expressly provided herein, no duties, responsibilities or liabilities are assumed, or shall be construed to be assumed, by the Trustee or the Collateral Agent by reason of this Supplemental Indenture. This Supplemental Indenture is executed and accepted by the Trustee and the Collateral Agent subject to all the terms and conditions set forth in the Indenture with the same force and effect as if those terms and conditions were repeated at length herein and made applicable to the Trustee and the Collateral Agent with respect hereto. The Trustee and the Collateral Agent make no representation as to the validity or sufficiency of this Supplemental Indenture.

Section 7. Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 8. Counterparts. The parties may sign any number of copies of this Supplemental Indenture. Each signed copy shall be an original, but all of such executed copies together shall represent the same agreement. Signature of the parties hereto transmitted by facsimile or PDF shall be deemed to be their original signatures for all purposes.

[Signatures on following pages]  

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