(Amendment No. 2)*

Under the Securities Exchange Act of 1934

(Name of Issuer)

(Title of Class of Securities)

(CUSIP Number)

(Name, Address and Telephone Number of Person
Authorized to Receive Notices and Communications)

(Date of Event Which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report the acquisition that is the subject of this Schedule 13D, and is filing this schedule because of §§240.13d–1(e), 240.13d–1(f) or 240.13d–1(g), check the following box. o

Note: Schedules filed in paper format shall include a signed original and five copies of the schedule, including all exhibits. See Rule 13d–7 for other parties to whom copies are to be sent.

* The remainder of this cover page shall be filled out for a reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed to be “filed” for the purpose of section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

(1)         See Item 3 for additional information.

(2)         Consists of (a) 22,148 Shares and 18,000 Shares issuable upon the exchange of $185,000 aggregate principal amount of Exchangeable Bonds, in each case individually owned by Mr. Mohn, (b) 2,054 Shares and 1,654 Shares issuable upon the exchange of $17,000 aggregate principal amount of Exchangeable Bonds, in each case individually owned by Mr. Mohn’s spouse, and (c) 33,096,351 Shares and 34,600,082 Shares issuable upon exchange of $355,611,000 aggregate principal amount of Exchangeable Bonds (which are exchangeable into Shares at the Initial Exchange Rate), in each case held directly by Perestroika (Cyprus) Ltd.

(3)         The percentage is based upon the 461,715,265 Shares outstanding as of April 24, 2018 as disclosed by the Issuer in the Issuer’s Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission on May 1, 2018.

2

(1)         See Item 3 for additional information.

(2)         Consists of 33,096,351 Shares and 34,600,082 Shares issuable upon exchange of $355,611,000 aggregate principal amount of Exchangeable Bonds (which are exchangeable into Shares at the Initial Exchange Rate), in each case held directly by Perestroika (Cyprus) Ltd.

(3)         The percentage is based upon the 461,715,265 Shares outstanding as of April 24, 2018 as disclosed by the Issuer in the Issuer’s Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission on May 1, 2018.

3

(1)         See Item 3 for additional information.

(2)         Consists of 33,096,351 Shares and 34,600,082 Shares issuable upon exchange of $355,611,000 aggregate principal amount of Exchangeable Bonds (which are exchangeable into Shares at the Initial Exchange Rate).

(3)         The percentage is based upon the 461,715,265 Shares outstanding as of April 24, 2018 as disclosed by the Issuer in the Issuer’s Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission on May 1, 2018.

4

This Amendment No. 2 to Schedule 13D (this “Amendment”) relates to the shares, par value CHF 0.10 per share (the “Shares”), of Transocean Ltd., a company organized under the laws of Switzerland (the “Issuer”). This Amendment amends the statement on Schedule 13D previously jointly filed by Frederik W. Mohn (“Mr. Mohn”) and Perestroika AS, a Norwegian private limited company (“Perestroika”) with the Securities and Exchange Commission on February 5, 2018, as previously amended (the “Prior Schedule 13D”).  Unless set forth in this Amendment, all Items are unchanged from the Prior Schedule 13D.  Capitalized terms used and not defined herein shall have the meanings ascribed to them in the Prior Schedule 13D.

The Reporting Persons (as defined below) are filing this Amendment to report the transfer of Shares directly owned by Perestroika to Perestroika (Cyprus) Ltd., a Cyprus private limited company and a wholly owned subsidiary of Perestroika (“Perestroika Sub”).

Item 3.                             Source and Amount of Funds or Other Consideration.

Item 3 is hereby amended by deleting the final paragraph of adding the following:

On March 16, 2018, Perestroika transferred 32,436,351 of its Shares and all of its Exchangeable Bonds to Perestroika Sub at a price of $9.54 per Share and 100% of the principal amount of Exchangeable Bonds transferred.  Each of these purchases were made using cash from an intercompany loan maintained between Perestroika and Perestroika Sub.  These purchases represent a change in the form of Mr. Mohn’s and Perestroika’s beneficial ownership, but do not change the overall amount of Shares or Exchangeable Bonds beneficially owned by Mr. Mohn or Perestroika.

On June 26, 2018, Perestroika transferred 660,000 of its Shares to Perestroika Sub at a price of $12.26 per Share.  Each of these purchases were made using cash from an intercompany loan maintained between Perestroika and Perestroika Sub.  These purchases represent a change in the form of Mr. Mohn’s and Perestroika’s beneficial ownership, but do not change the overall amount of Shares beneficially owned by Mr. Mohn or Perestroika.

Item 5.                             Interest in Securities of the Issuer.

Item 5 is deleted in its entirety and replaced with the following:

(a)                                 The aggregate number and percentage of Shares (including Shares issuable upon the exchange of the Exchangeable Bonds at the Initial Exchange Rate) beneficially owned by the Reporting Persons are as follows (based upon 461,715,265 Shares outstanding as of April 24, 2018 as disclosed by the Issuer in the Issuer’s Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission on May 1, 2018):

(i)                                     Mr. Mohn beneficially owns 67,740,289 Shares, or approximately 13.6%.

(ii)                                  Perestroika and Perestroika Sub each beneficially own 67,696,433 Shares, or approximately 13.6%.

(b)                              Mr. Mohn has:

5

(i)                                     sole power to vote or direct the vote of 43,856 Shares;

(ii)                                  shared power to vote or direct the vote of 67,696,433 Shares;

(iii)                               sole power to dispose or direct the disposition of 43,856 Shares; and

(iv)                              shared power to dispose or direct the disposition of 67,696,433 Shares.

Perestroika and Perestroika Sub each have:

(i)                                     sole power to vote or direct the vote of 0 Shares;

(ii)                                  shared power to vote or direct the vote of 67,696,433 Shares;

(iii)                               sole power to dispose or direct the disposition of 0 Shares; and

(iv)                              shared power to dispose or direct the disposition of 67,696,433 Shares.

(c)                                  Except as described in Item 3 of the Prior Schedule 13D as amended by this Amendment, there have been no reportable transactions with respect to the Shares within the last 60 days by the Reporting Persons.

(d)                                 Except as set forth herein, no other person is known by the Reporting Persons to have the right to receive or the power to direct the receipt of dividends from, or the proceeds from the sale of, Shares and Exchangeable Bonds beneficially owned by the Reporting Persons.

(e)                                  Not applicable.

6

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this Statement is true, complete and correct.

Dated: July 3, 2018

7