SUPPLEMENT TO WARRANT AGREEMENT

Exhibit 4.1

SUPPLEMENT TO WARRANT AGREEMENT

THIS SUPPLEMENT TO WARRANT AGREEMENT, dated as of December 18, 2008 (the “Supplement”), by and among Transocean Ltd., a Swiss corporation (the “Parent”), Transocean Inc. (formerly Transocean Sedco Forex Inc.), a company incorporated under the laws of the Cayman Islands (the “Company”), and The Bank of New York, a bank and trust company organized and existing under the laws of New York (the “Warrant Agent”), successor to the American Stock Transfer & Trust Company.

WHEREAS, pursuant to the Warrant Agreement dated as of April 22, 1999 (the “Warrant Agreement”), by and between R&B Falcon Corporation, a Delaware corporation (“R&B Falcon”), and the American Stock Transfer & Trust Company, a bank and trust company organized and existing under the laws of New York (the “Predecessor Warrant Agent”), R&B Falcon appointed the Predecessor Warrant Agent to act as agent for R&B Falcon in connection with the issuance, exchange, cancellation, replacement and exercise of warrants (the “Warrants”) to purchase 35 shares of common stock, par value $0.01 per share, of R&B Falcon (“R&B Falcon Common Stock”) issued pursuant to the Warrant Agreement at an exercise price of $9.50 per share of R&B Falcon Common Stock; and

WHEREAS, pursuant to an Agreement and Plan of Merger, dated as of August 19, 2000, by and among the Company, Transocean Holdings Inc., a Delaware corporation and a wholly owned subsidiary of the Company (“Sub”), TSF Delaware Inc., a Delaware corporation and a wholly owned subsidiary of Sub, and R&B Falcon (i) each outstanding share of R&B Falcon Common Stock was converted into the right to receive 0.5 ordinary shares, par value $0.01 per share, of the Company (“Company Ordinary Shares”) and (ii) R&B Falcon became an indirect wholly owned subsidiary of the Company; and

WHEREAS, pursuant to a Supplement to Warrant Agreement, dated as of January 31, 2001 (the “2001 Supplement”), the Company assumed the Warrants and the Warrants became exercisable for 17.5 Company Ordinary Shares at an exercise price of $19.00 per Company Ordinary Share; and

WHEREAS, pursuant to an Agreement and Plan of Merger, dated as of July 21, 2007, by and among the Company, GlobalSantaFe Corporation, a company incorporated under the laws of the Cayman Islands, and Transocean Worldwide Inc., a company incorporated under the laws of the Cayman Islands and a direct wholly owned subsidiary of the Company, each outstanding Company Ordinary Share was reclassified as, and converted into, (i) 0.6996 validly issued, fully paid and nonassessable Company Ordinary Shares, and (ii) $33.03 in cash (the “Reclassification”); and

WHEREAS, pursuant to Sections 17(a) and (c) of the Warrant Agreement, upon consummation of the Reclassification, the Warrants became exercisable for 12.243 Company Ordinary Shares at an exercise price of $21.74 per Company Ordinary Share; and

WHEREAS, pursuant to an Amendment to Warrant Agreement, dated as of November 27, 2007 (the “Reclassification Amendment”), each Warrant became exercisable for, at the election of the holder of such Warrant, subject to the provisions contained in the Warrant

Agreement and in the certificate evidencing such Warrant, 12.243 Company Ordinary Shares and $578.025 at an exercise price of $19.00 per Company Ordinary Share for which such Warrant was exercisable prior to consummation of the Reclassification in lieu of the adjustment of such Warrant pursuant to Section 17 of the Warrant Agreement in connection with the Reclassification; and

WHEREAS, pursuant to an Agreement and Plan of Merger, dated as of October 9, 2008 (as amended, the “Merger Agreement”), by and among the Company, the Parent and Transocean Cayman Ltd., a company incorporated under the laws of the Cayman Islands and a direct wholly owned subsidiary of the Parent (“Transocean-Acquisition”), (i) the Company merged by way of schemes of arrangement under Cayman Islands law with Transocean-Acquisition, with the Company as the surviving company (the “Merger”), (ii) the Company became a direct, wholly owned subsidiary of the Parent and (iii) each outstanding Company Ordinary Share was exchanged for one registered share, par value 15.00 Swiss francs per share, of the Parent (“Parent Shares”); and

WHEREAS, pursuant to Section 3.3 of the Merger Agreement, the Parent has assumed the Warrants.

NOW, THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereto agree as follows:

1. The Parent hereby assumes all obligations of the Company under the Warrant Agreement and agrees to be bound by all of the provisions thereof, as amended by the 2001 Supplement, the Reclassification Amendment and this Supplement.

2. In accordance with Section 17(l) of the Warrant Agreement, each Warrant shall represent the right, subject to the provisions contained in the Warrant Agreement and in the certificate evidencing such Warrant, to purchase from the Parent (and the Parent shall deliver, or cause a subsidiary of the Parent to deliver, to such holder of the Warrant) 12.243 Parent Shares (the “Warrant Shares”) on exercise of such Warrant and payment of the exercise price of $21.74 per Warrant Share (the “Exercise Price”).

3. In accordance with the Reclassification Amendment and Section 17(l) of the Warrant Agreement, each Warrant, at the election of the holder of such Warrant, shall represent the right, subject to the provisions contained in the Warrant Agreement and in the certificate evidencing such Warrant, to purchase from the Parent (and the Parent shall deliver, or cause a subsidiary of the Parent to deliver, to such holder of the Warrant) 12.243 Parent Shares and to receive (and the Parent shall deliver, or cause a subsidiary of the Parent to deliver, to such holder of the Warrant) $578.025 on exercise of such Warrant and payment of the exercise price of $19.00 per Company Ordinary Share for which such Warrant was exercisable prior to consummation of the Reclassification in lieu of the adjustment of the exercise price or the number of Warrant Shares issuable upon the exercise of such Warrant pursuant to Section 17 of the Warrant Agreement in connection with the Reclassification.

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4. Notwithstanding anything in the Warrant Agreement or this Supplement to the contrary, in no event shall the Warrant Agent be liable to the Parent or the Company for special, indirect, punitive, incidental or consequential loss or damage of any kind whatsoever (including but not limited to lost profits), even if the Warrant Agent has been advised of the likelihood of such loss or damage and regardless of the form of the action. In furtherance thereof, in the event that the Warrant Agent shall incur any liability or be subject to any special, indirect, punitive, incidental or consequential losses or damages of any kind whatsoever (including but not limited to lost profits) arising from any suit, action or proceeding brought by any holder of Warrants or any third party in connection with the Warrants, the Warrant Agreement or this Supplement, then the Parent and the Company shall indemnify the Warrant Agent for such losses or damages, even if the Warrant Agent has been advised of the likelihood of such losses or damages and regardless of the form of the action, and even if such losses or damages result from the Warrant Agent’s gross negligence; provided, however, that the Parent and the Company shall have no obligation to indemnify the Warrant Agent for such losses or damages that result from the Warrant Agent’s bad faith or willful misconduct. Any liability of the Warrant Agent will be limited to two (2) times the amount of fees paid by the Parent or its predecessors under the Warrant Agreement.

5. Except as expressly supplemented and amended hereby, the terms and conditions of the Warrant Agreement shall remain in full force and effect.

6. To the extent that any provision hereof conflicts with any provision of the Warrant Agreement, the provision hereof shall control.

7. Notwithstanding the date of execution hereof, this Supplement shall be deemed effective as of the Effective Time (as defined in the Merger Agreement) and if such Effective Time does not occur, this Supplement shall be void and of no force or effect.

8. This Supplement shall be governed by and construed in accordance with the laws of New York.

9. This Supplement may be executed in counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

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IN WITNESS WHEREOF, the parties hereto have caused this Supplement to be duly executed, as of the day and year first above written.

TRANSOCEAN LTD.
By:		/s/ Xxxx X. Xxxxx
Name:		Xxxx X. Xxxxx
Title:		Senior Vice President and General Counsel

TRANSOCEAN INC.
By:		/s/ Xxxx X. Xxxxx
Name:		Xxxx X. Xxxxx
Title:		Senior Vice President and General Counsel

THE BANK OF NEW YORK
By:		/s/ Xxxxxx Xxxxx
Name:		Xxxxxx Xxxxx
Title:		Vice President