Exhibit 4.1

This FIRST SUPPLEMENTAL INDENTURE, dated as of May 8, 2024 (this “Supplemental Indenture”), is entered into among Transocean Titan Financing Limited (the “Company”), each of the Guarantors (as defined in the Indenture referred to below) signatory hereto and Truist Bank, as Trustee and Collateral Agent.

RECITALS

WHEREAS, the Company, the Guarantors, the Trustee and the Collateral Agent entered into an Indenture, dated as of January 17, 2023 (as heretofore amended, supplemented or otherwise modified, the “Indenture”), providing for the issuance of the Company’s 8.375% Senior Secured Notes due 2028 (the “Securities”);

WHEREAS, the Indenture provides that under certain circumstances the Indenture may be amended with the consent of the Holders of at least a majority in principal amount of the Outstanding Securities affected;

WHEREAS, in accordance with Section 10.02 of the Indenture, the Company has received the consent of the Holders of at least a majority in principal amount of the Outstanding Securities to amend the Indenture as set forth herein, which consents have not been withdrawn;

WHEREAS, the Company, pursuant to the foregoing authority, desires to amend the Indenture in certain respects as set forth herein and has requested the Trustee and the Collateral Agent join with it and the Guarantors in the execution and delivery of this Supplemental Indenture; and

WHEREAS, all acts and things prescribed by the Indenture necessary to make this Supplemental Indenture a valid and legally binding instrument according to its terms, and a valid and legally binding supplement to the Indenture, have been done and performed.

NOW, THEREFORE, in consideration of the mutual agreements and covenants set forth herein, the parties hereto agree, subject to the terms and conditions hereinafter set forth, as follows for the benefit of the Trustee, the Collateral Agent and the Holders (as defined in the Indenture):

ARTICLE I

Section 1.01.Capitalized terms used herein without definition shall have the meanings ascribed to them in the Indenture.

Section 1.02.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.

ARTICLE II

Section 2.01.Amendments.

(a)  Section 1.01 of the Indenture is hereby amended by amending and restating the definition of “Collateral Rig Net Income” to read as follows:

“Collateral Rig Net Income” means, for any period (subject to the last two sentences of this definition), the combined revenue of the Collateral Rig Owner and the Collateral Rig Operator attributable to the Collateral Rig (including, for the avoidance of doubt, such revenue related to the Drilling Contract) for such period minus operating expenses attributable to the Collateral Rig for such period (including allocated overhead expenses).  Collateral Rig Net Income shall be annualized for the fiscal periods ending September 30, 2024 and December 31, 2024 (such annualization to be calculated as follows: for the period ended September 30, 2024, the amount for the two quarters then ended shall be multiplied by two; and for the period ended December 31, 2024, the amount for

the three quarters then ended shall be multiplied by four thirds).  For the avoidance of doubt, references in this definition to the Collateral Rig Owner and the Collateral Rig Operator shall include their respective predecessors that are Subsidiaries of Holdings and owned and/or operated the Collateral Rig.

(b) Section 4.14 of the Indenture is hereby amended and restated as follows:

Section 4.14.Collateral Rig Leverage Ratio.

The Company will not permit the Collateral Rig Leverage Ratio as of the last day of each fiscal period of Holdings specified below to exceed the corresponding ratio set forth below:

Fiscal Periods EndingMaximum Collateral Rig Leverage Ratio

September 30, 2024 and December 31, 20245.75:1.00

March 31, June 30, September 30 and December 31, 20255.00:1.00

March 31, June 30, September 30 and December 31, 20264.25:1.00

March 31, June 30, September 30 and December 31, 20273.50:1.00

Neither the Trustee nor the Collateral Agent shall be obligated to monitor or confirm, on a continuing basis or otherwise, the Company’s compliance with this Section 4.14 (as to which the Trustee and the Collateral Agent are entitled to rely exclusively on the quarterly compliance certificate delivered by the Company pursuant to Section 4.09(b)).

ARTICLE III

Section 3.01.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 3.02.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 3.03.THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

Section 3.04.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]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first above written.

TRANSOCEAN TITAN FINANCING LIMITED, as Company

By: /s/ Simone Ramcharitar

Name: Simone Ramcharitar

Title: Vice President

TRANSOCEAN INC., as Guarantor

By: /s/ Simone Ramcharitar

Name: Simone Ramcharitar

Title: Vice President

TRANSOCEAN LTD., as Guarantor

By: /s/ Sandro Thoma

Name: Sandro Thoma

Title: Corporate Secretary

TRITON TITAN GMBH., as Guarantor

By: /s/ Paul Tranter

Name: Paul Tranter

Title: Chairman of the Board of Managing Directors

Signature Page to First Supplemental Indenture

TRUIST BANK, as Trustee and as Collateral Agent

By: /s/ Patrick Giordano

Name: Patrick Giordano

Title: Vice President

Signature Page to First Supplemental Indenture