Transocean (RIG) 10-K 2011 FY Annual report

Exhibit 32.1

CERTIFICATION PURSUANT TO SECTION 906 OF

THE SARBANES-OXLEY ACT OF 2002 (SUBSECTIONS (a) AND (b)

OF SECTION 1350, CHAPTER 63 OF TITLE 18, UNITED STATES CODE)

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (Subsections (a) and (b) of Section 1350, Chapter 63 of Title 18, United States Code), I, Steven L. Newman, President and Chief Executive Officer of Transocean Ltd., a Swiss corporation (the “Company”), hereby certify, to my knowledge, that:

(1) the Company’s Annual Report on Form 10-K for the year ended December 31, 2011 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated:           February 27, 2012 /s/ Steven L. Newman                                                                                                     Steven L. Newman President and Chief Executive Officer