Exhibit 4.2

EXECUTION VERSION

AMENDMENT TO

REGISTRATION RIGHTS AGREEMENT

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This Amendment to Registration Rights Agreement (this “Amendment”) is made as of August 14, 2020 (the “Amendment Date”) and amends that certain Registration Rights Agreement, dated January 30, 2018 (the “Original Agreement”) between Transocean Ltd., a corporation incorporated under the laws of Switzerland (“Transocean”), and Transocean Inc., an exempted company incorporated under the laws of the Cayman Islands (“TINC”), on one hand, and the several persons listed on Schedule I thereto, on the other. Capitalized terms used but not defined herein have the meanings ascribed to them in the Original Agreement.

WHEREAS, pursuant to Section 11(k) of the Original Agreement, the Original Agreement may be amended, modified or supplemented with the written consent of the Company and a Majority of the Securityholders thereunder;

WHEREAS, Perestroika AS beneficially owns a majority of the Registrable Securities, and therefore constitutes a Majority of the Securityholders; and

WHEREAS, the Company and a Majority of the Securityholders thereunder desire to amend the Original Agreement as set forth herein (such Original Agreement, as amended by this Amendment,  the “Amended Agreement”).

NOW, THEREFORE, in consideration of the mutual covenants and agreements herein contained and other good and valid consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Amendment hereby agree as follows:

1. Amendments to Section 1(a).

a. Section 1(a) of the Original Agreement is hereby amended to include the following definition of “New Exchangeable Bonds” and to replace in its entirety the definition of “Company”:

i. “New Exchangeable Bonds” means the 2.5% Senior Guaranteed Exchangeable Bonds due 2027 to be issued by TINC, including the guarantee thereof by Transocean and the subsidiary guarantors from time to time party thereto.  Any reference to Exchangeable Bonds shall be read to be to New Exchangeable Bonds.

ii. “Company” means Transocean, with respect to any securities issued by Transocean, and TINC, with respect to any securities issued by TINC.  For the avoidance of doubt, with respect to the New Exchangeable Bonds, “Company” means each of TINC, as issuer of the New Exchangeable Bonds, and Transocean, as issuer of the related guarantee.

iii. “Perestroika” means Perestroika AS and any of its Affiliates.

b. The definition of Registrable Securities set forth in Section 1(a) of the Original Agreement is hereby replaced in its entirety with the following definition:

i. “Registrable Securities” means, at any time, (i) all Shares held by a party hereto issued upon exchange of the New Exchangeable Bonds or (ii) with respect to Perestroika AS, all Shares owned by Perestroika AS, whether owned as of the date hereof or acquired in the manner set forth in clause (i) or thereafter at any time prior to the first time when Perestroika AS no longer

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owns any Registrable Securities, (iii) all Shares issued or issuable after the date hereof with respect to the Shares referred to in clauses (i) and (ii) by way of stock dividend or stock split or in connection with a combination of stock, recapitalization, merger, consolidation or other reorganization or otherwise, and (iv) all Shares issued by the issuer thereof in exchange or replacement of any securities referred to in clauses (i), (ii) and (iii); provided that Registrable Securities shall not include any Shares or other securities referred to in clauses (i) through (iv) that (1) have been sold pursuant to an effective registration statement or Rule 144 under the Securities Act or are eligible to be sold pursuant to Rule 144 under the Securities Act without regard to any limitations contained thereunder, no longer bear a restricted legend and, if requested by the holder thereof, have been transferred into the clearing system through which freely transferable securities of that class are primarily held, under the same securities identification number as such other securities (2) have been sold to someone other than a Securityholder in a transaction as a result of which a subsequent public distribution of such securities would not require registration under the Securities Act, no longer bear a restricted legend and, if requested by the holder thereof, have been transferred into the clearing system through which freely transferable securities of that class are primarily held, under the same securities identification number as such other securities (3) have been sold to someone other than a Securityholder in a transaction that was not permitted pursuant to Section 9, or (4) are not outstanding. To avoid doubt, all Shares issued upon exchange of Exchangeable Bonds will be issued under Section 3(a)(9) of the Securities Act and are entitled to tacking under Rule 144 of the Securities Act to any holding period of the associated Exchangeable Bonds, in each case in accordance with public guidance previously issued by the SEC.

2. Amendments to Section 2(a).

a. Section 2(a) of the Original Agreement is hereby amended by adding the following language at the end of the current text:

i. ; provided that the Company’s obligation to use reasonable best efforts shall not be violated if within 30 days of the issuance of the New Exchangeable Bonds, the Company files with the SEC a Resale Shelf Registration Statement.

3. Amendments to Section 4(a).

a. Section 4(a)(i) of the Original Agreement is hereby amended by adding “and, solely with respect to Perestroika, Seward & Kissel LLP” after “Cleary Gottlieb Steen & Hamilton LLP”.

b. Section 4(a)(ii) of the Original Agreement is hereby amended by adding the following language at the end of the current text:

i. use reasonable best efforts to keep the Prospectus updated, upon the written request of Perestroika, by filing a prospectus supplement with the SEC to register any Registrable Securities that Perestroika acquires subsequent to the filing of the Registration Statement; provided that the Company will not be required to file more than one prospectus supplement pursuant to this Section 4(a)(ii) in any calendar quarter and not more than a total of two prospectus supplements in any twelve month period;

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4. Amendment to Section 11(k).

a. Section 11(k) of the Original Agreement is hereby amended by adding the following language at the end of the current text:

i. ; provided, however, that so long as Perestroika AS is a Securityholder, any amendment, modification or supplement that is materially adverse to Perestroika shall require the prior written consent of Perestroika AS.

5. Amendment to Schedule 1.

a. Schedule 1 of the Original Agreement is hereby replaced in its entirety with Schedule 1 attached hereto.

6. No Additional Changes. Except as expressly and specifically set forth in this Amendment, all provisions in the Original Agreement shall remain in full force and effect according to their terms, and the Securityholders shall continue to be bound by such Original Agreement as modified by this Amendment. In the event of any conflict between any provision of the Original Agreement and this Amendment, this Amendment shall control. From and after the date hereof, all references in the Original Agreement to “this Agreement” shall mean the Amended Agreement.

7. Counterparts; Effectiveness. This Amendment may be executed in any number of counterparts (including by e-mail or facsimile) and by different parties hereto in separate counterparts, with the same effect as if all parties had signed the same document. All such counterparts shall be deemed an original, shall be construed together and shall constitute one and the same instrument. This Amendment shall become effective when each party hereto shall have received counterparts hereof signed by all of the other parties hereto.

8. Governing Law. This Amendment shall be governed by and construed in accordance with the law of the State of New York.

[Signature Pages Follow]

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IN WITNESS WHEREOF, this Amendment has been duly executed by each of the parties hereto as of the Amendment Date.

Transocean Ltd.

By: /s/Sandro Thoma

Name: Sandro Thoma
Title: Corporate Secretary

Transocean Inc.

By: /s/Simone Ramcharitar

Name: Simone Ramcharitar
Title: Vice President

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PERESTROIKA (CYPRUS) LTD.

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By: /s/Frederik W. Mohn
Name: Frederik W. Mohn
Title: Director

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Schedule 1

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