Pricing Supplement No. 12 dated November 3, 1998           Rule 424(b)(3)
(To Prospectus dated April 1, 1996                         File No. 33-58887
and Prospectus Supplement dated April 1, 1996)

                            Colgate-Palmolive Company

                         Medium-Term Notes - Fixed Rate

                                    Series C

    We are hereby offering to sell Notes having the terms specified below to you
with the  assistance of Salomon Smith Barney Inc.,  acting as agent,  at a fixed
initial public offering price of 99.957% of the Principal Amount.

Principal Amount: $20,000,000            Original Issue Date:   November 6, 1998
Interest Rate:    5.65% per annum        Net Proceeds to Company:  $19,991,400
Stated Maturity Date: December 1, 2011   Agent's Discount or Commission:  See
                                         "Supplemental Plan of Distribution"
                                         below.

Interest Payment Dates: Semi-Annually (See "Other Provisions - Interest" below).

Redemption:
         [ X ] The Notes  cannot be redeemed by the
               Company  prior  to the  Stated  Maturity Date.
         [   ] The Notes may be redeemed by the Company prior to the Stated
               Maturity Date. Initial Redemption Date:

               Initial Redemption Percentage:   ____%

               Annual Redemption Percentage Reduction: ____% until Redemption 
               Percentage is 100% of the Principal amount.

Optional Repayment:
         [ X ]        The Notes cannot be repaid at the option of the holder
                      thereof prior to the Stated Maturity Date.
         [   ]        The Notes can be repaid at the option of the holder
                      thereof prior to the Stated Maturity Date at
                      Optional Repayment Date(s):

                      Repayment Price: _____%

Currency:
         Specified Currency:        U.S. dollars
                 (If other than U.S. dollars, see attached.)
         Minimum Denomination: $___________

         (Applicable only if Specified Currency is other than U.S. dollars.)

Original Issue Discount: [   ]      Yes     [ X ]    No
         Total amount of OID:
         Yield to Maturity:
         Initial Accrual Period:

Form:        [ X ]    Book-entry      [   ]        Certificated

 [ X ]        Other provisions:



Interest:

         Interest  on the Notes will  accrue  from  November 6, 1998 and will be
         payable in U.S.  dollars on the first day of June and  December of each
         year,  commencing  June 1, 1999 up to and including the Stated Maturity
         Date (each, an "Interest Payment Date").  Interest will accrue from and
         including  each Interest  Payment Date (or from November 6, 1998, if no
         interest has been paid or duly  provided for) to but excluding the next
         succeeding Interest Payment Date. In the event an Interest Payment Date
         falls on a day other than a Business Day,  interest will be paid on the
         next  succeeding  Business  Day and no interest on such  payment  shall
         accrue for the period from and after such Interest Payment Date to such
         next succeeding Business Day.

Use of Proceeds:
- ---------------
         The net proceeds from the sale of the Notes will be used by the Company
         to retire  commercial paper which was issued by the Company for general
         corporate  purposes and working  capital.  As of October 30, 1998,  the
         Company's outstanding  commercial paper had a weighted average interest
         rate of 5.2904% with maturities ranging from 3 to 89 days.

Supplemental Plan of Distribution:
- ---------------------------------
         Salomon  Smith Barney Inc.,  the agent,  will receive no  commission in
         respect of the sale of the Notes.  An affiliate of Salomon Smith Barney
         Inc.  may receive  compensation  in  connection  with a swap  agreement
         entered into with the Company.