FORM 4
                                             _________________________________
                                             |          OMB APPROVAL         |
[ ] Check this box if no longer subject      _________________________________
    to Section 16. Form 4 or Form 5          | OMB Number:         3235-0287 |
    obligations may continue.  See           | Expires:     January 31, 2005 |
    Instruction 1(b).                        | Estimated average burden      |
                                             | hours per response....... 0.5 |
                                             _________________________________


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


                 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP

    Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
       Section 17(a) of the Public Utility Holding Company Act of 1935 or
              Section 30(f) of the Investment Company Act of 1940

(Print or Type Responses)
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1. Name and Address of Reporting Person*

   Stevens            John
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   (Last)            (First)

   c/o Moore Corporation Limited
   One Canterbury Green
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                     (Street)

   Stamford              CT              06901
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   (City)               (State)         (Zip)

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2. Issuer Name and Ticker or Trading Symbol

   Moore Corporation Limited (MCL)
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3. I.R.S. Identification Number of Reporting Person, if an entity (voluntary)



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4. Statement for Month/Day/Year

   August 27, 2002
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5. If Amendment, Date of Original (Month/Day/Year)



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6. Relationship of Reporting Person(s) to Issuer (Check all applicable)

   [X] Director                             [ ] 10% Owner
   [ ] Officer (give title below)           [ ] Other (specify below)


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7. Individual or Joint/Group Filing (Check Applicable Line)

   [X] Form filed by One Reporting Person
   [ ] Form filed by More than One Reporting Person

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                        TABLE I -- NON-DERIVATIVE SECURITIES ACQUIRED, DISPOSED OF, OR BENEFICIALLY OWNED
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                                                                                       5. Amount of     6. Owner-
                                                                                          Securities       ship
                  2. Trans-   2A. Deemed      3. Trans-    4. Securities Acquired (A)     Beneficially     Form:
                     action       Execution      action       or Disposed of (D)          Owned            Direct      7. Nature of
                     Date         Date,          Code         (Instr. 3, 4 and 5)         Following        (D) or         Indirect
1. Title of          (Month/      if any      (Instr. 8)   --------------------------     Reported         Indirect       Beneficial
   of Security       Day/         (Month/     ----------   Amount    (A) or     Price     Transaction(s)   (I)            Ownership
   (Instr. 3)        Year)        Day/Year)   Code    V              (D)                 (Instr. 3 and 4)  (Instr. 4)     (Instr. 4)
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Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.                   (over)
* If the form is filed by more than one reporting person, see Instruction 4(b)(v).                                   SEC 1474 (9-02)



POTENTIAL PERSONS WHO ARE TO RESPOND TO THE COLLECTION OF INFORMATION CONTAINED
IN THIS FORM ARE NOT REQUIRED TO RESPOND UNLESS THE FORM DISPLAYS A CURRENTLY
VALID OMB CONTROL NUMBER





FORM 4 (CONTINUED)



                           TABLE II -- DERIVATIVE SECURITIES ACQUIRED, DISPOSED OF, OR BENEFICIALLY OWNED
                                    (E.G. PUTS, CALLS, WARRANTS, OPTIONS, CONVERTIBLE SECURITIES)
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    1.        2.        3.     3A.        4.        5.             6.            7.          8.        9.         10.       11.
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                                                                            Title and              Number of   Ownership
                                                Number of     Date Exer-    Amount of              derivative  Form of
                                                Derivative    cisable and   Underlying             Securities  Deriv-
                               Deemed           Securities    Expiration    Securities     Price   Benefi-     ative
            Conver-            Execu-  Trans-   Acquired (A)  Date (Month/  (Instr. 3      of      cially      Security
            sion or   Trans-   tion    action   or Disposed    Day/Year)     and 4)        Deriv-  Owned       Direct
            Exercise  action   Date,   Code     of (D)        ------------ --------------  ative   Following   (D) or    Nature of
Title of    Price of  Date     if any  (Instr.  (Instr. 3,    Date                 Amount  Secur-  Reported    Indirect  Indirect
Derivative  Deriv-    (Month/  (Month/  8)       4 and 5)     Exer- Expir-         or Num- ity     Tran-       (I)       Beneficial
Security    ative      Day/    Day/    -------  ----------    cis-  ation          ber of  (Instr. saction(s)  (Instr.   Ownership
(Instr. 3)  Security   Year)   Year)   Code  V  (A)   (D)     able  Date    Title  Shares   5)     (Instr. 4)   4)       (Instr. 4)
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Deferred     $10.37   08/27/02  N/A     A       602.7         N/A    NA    Common   602.7   ONE     8,318.21      D        N/A
Share Units                                                                Shares           FOR
(Non-                                                                                       ONE
voting,
non-
transfer-
rable unit
equivalent
to Common
Shares)
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Explanation of Responses:

              /s/ John W. Stevens                             Sept. 9, 2002
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              ** Signature of Reporting Person                    Date


** Intentional misstatements or omissions of facts constitute Federal Criminal
   Violations.  See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).

Note: File three copies of this Form, one of which must be manually signed.
      If space is insufficient, see Instruction 6 for procedure.



Potential persons who are to respond to the collection of information contained
in this form are not required to respond unless the form displays a currently
valid OMB Number.