Statement of Changes in Beneficial Ownership (4)

FORM 4

[ ] Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES

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Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934 or Section 30(h) of the Investment Company Act of 1940

1. Name and Address of Reporting Person * Perestroika	2. Issuer Name and Ticker or Trading Symbol Transocean Ltd. [ RIG ]	5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director                    __X__ 10% Owner _____ Officer (give title below)    _____ Other (specify below)
(Last)          (First)          (Middle) TURMSTRASSE 30	3. Date of Earliest Transaction (MM/DD/YYYY) 6/15/2021
(Street) STEINHAUSEN, V8 6312 (City)        (State)        (Zip)	4. If Amendment, Date Original Filed (MM/DD/YYYY)	6. Individual or Joint/Group Filing (Check Applicable Line) _X _ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person

Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned
1.Title of Security (Instr. 3)	2. Trans. Date	2A. Deemed Execution Date, if any	3. Trans. Code (Instr. 8)		4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5)			5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4)	6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4)	7. Nature of Indirect Beneficial Ownership (Instr. 4)
			Code	V	Amount	(A) or (D)	Price
Registered Shares	6/15/2021		P		3000000	A	$4.17 (1)	70740354	D (3)
Registered Shares	6/16/2021		P		2000000	A	$4.20 (2)	72740354	D (3)

Table II - Derivative Securities Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities)
1. Title of Derivate Security (Instr. 3)	2. Conversion or Exercise Price of Derivative Security	3. Trans. Date	3A. Deemed Execution Date, if any	4. Trans. Code (Instr. 8)		5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5)		6. Date Exercisable and Expiration Date		7. Title and Amount of Securities Underlying Derivative Security (Instr. 3 and 4)		8. Price of Derivative Security (Instr. 5)	9. Number of derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)	10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)	11. Nature of Indirect Beneficial Ownership (Instr. 4)
				Code	V	(A)	(D)	Date Exercisable	Expiration Date	Title	Amount or Number of Shares

Explanation of Responses:
(1)	The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $4.02 to $4.255, inclusive. The reporting person undertakes to provide Transocean Ltd. (the "Company"), any security holder of the Company, or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of shares sold at each separate price within the ranges set forth in footnotes (1) and (2) to this Form 4.
(2)	The price reported in Column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $4.09 to $4.29, inclusive.
(3)	These securities are held directly by Perestroika AS. Mr. Frederik Mohn is a sole director and owner of Perestroika AS and is the beneficial owner of all securities owned by Perestroika AS.

Remarks: Perestroika (Cyprus) Ltd. is a wholly owned subsidiary of Perestroika AS. Due to Perestroika (Cyprus) Ltd.'s designation of a member of the board of directors of the Company, each of Perestroika (Cyprus) Ltd. and Perestroika AS, as its sole owner, may be deemed to be a director of the Company by deputization.

Reporting Owners
Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
Perestroika TURMSTRASSE 30 STEINHAUSEN, V8 6312	X	X

Signatures
Daniel Ro-Trock By Power of Attorney		6/17/2021
**Signature of Reporting Person		Date