FORM 4
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                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*

   OLIVA            THOMAS
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   (Last)            (First)

   c/o Moore Corporation Limited
   One Canterbury Green, 6th Floor
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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/Year

   10/21/02

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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)

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

     President, Forms and Labels Division
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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
                                                                                         Securities
                                                                                         Beneficially   6. Ownership
                             2A. Deemed      3. Trans-                                   Owned             Form:
                 2. Trans-       Execution      action     4. Securities Acquired        Following         Direct      7. Nature of
                    action       Date,          Code          (A) or Disposed of (D)     Reported          (D) or         Indirect
1. Title of         Date         if any         (Instr.       (Instr. 3, 4 and 5)        Transaction(s)    Indirect       Beneficial
   Security         (Month/      (Month/        8)         -------------------------     --------------    (I)            Ownership
   (Instr. 3)       Day/         Day/        ----------    Amount    (A) or    Price     (Instr. 3         ---------      ----------
                    Year)        Year)       Code    V               (D)                 and 4)            (Instr. 4)     (Instr. 4)
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Common Stock       10/17/02                   A             75,000     A                  160,745                D
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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 person, see Instruction 4(b)(v).                                             SEC 1474 (7-02)



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-
                                               Securities   Expiration       Securities     Price   Benefi-     ative
           Conver-                     Trans-  Acquired (A) Date (Month/     (Instr. 3      of      cially      Security:
           sion or  Trans-  Deemed     action  or Disposed   Day/Year)        and 4)        Deriv-  Owned       Direct
           Exercise action  Execution  Code    of (D)       --------------  --------------  ative   Following   (D) or    Nature of
Title of   Price of Date    Date,      (Instr. (Instr. 3,   Date                    Amount  Secur-  Reported    Indirect  Indirect
Derivative Deriv-   (Month/ if any,     8)      4 and 5)    Exer-    Expir-         or Num- ity     Trans-      (I)       Beneficial
Security   ative     Day/   (Month     ------- ----------   cis-     ation          ber of  (Instr. action(s)   (Instr.   Ownership
(Instr. 3) Security  Year)   Day/Year) Code  V (A)   (D)    able     Date   Title   Shares   5)     (Instr. 4)   4)       (Instr. 4)

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Explanation of Responses:

                   /s/ Thomas W. Oliva                       October 21, 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 provided 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.
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