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 *

THIGPEN JEREMY D
2. Issuer Name and Ticker or Trading Symbol

Transocean Ltd. [ RIG ]
5. Relationship of Reporting Person(s) to Issuer (Check all applicable)

__X__ Director                    _____ 10% Owner
__X__ Officer (give title below)    _____ Other (specify below)
President & CEO
(Last)          (First)          (Middle)

1414 ENCLAVE PARKWAY
3. Date of Earliest Transaction (MM/DD/YYYY)

5/8/2021
(Street)

HOUSTON, TX 77077
(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 5/8/2021  M  363636 (1)A$0 1473591 D  
Registered Shares 5/10/2021  F  146012 (2)D$3.94 1327579 D  

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 Security3. Trans. Date3A. Deemed Execution Date, if any4. 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 Date7. 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)
CodeV(A)(D)Date ExercisableExpiration DateTitleAmount or Number of Shares
Restricted Units $0 5/8/2021  M   363636     (1) (1)Registered Shares 363636 $0 727273 D  

Explanation of Responses:
(1) Restricted Units, which are 1-for-1 share equivalents, acquired on May 8, 2020, pursuant to the Issuer's long-term incentive plan. One third of such restricted units vested on May 8, 2021, resulting in the right of the reporting person to receive the registered shares. The remaining restricted share units vest as follows: 363,636 on March 1, 2022 and 363,637 on March 1, 2023.
(2) Shares sold upon vesting to satisfy tax obligations.

Reporting Owners
Reporting Owner Name / Address
Relationships
Director10% OwnerOfficerOther
THIGPEN JEREMY D
1414 ENCLAVE PARKWAY
HOUSTON, TX 77077
X
President & CEO

Signatures
/s/ Daniel Ro-Trock By Power of Attorney5/11/2021
**Signature of Reporting PersonDate

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