<PAGE>

                                  EXHIBIT 4.11

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE OR RECEIVABLE UPON THE
     EXERCISE OR CONVERSION THEREOF OR AS A RESULT OF THE OWNERSHIP HEREOF HAVE
     NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
     "ACT"), OR THE SECURITIES LAWS OF ANY STATE. THE SECURITIES MAY NOT BE
     TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER
     SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR PURSUANT TO AN APPLICABLE
     EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF SUCH ACT AND SUCH LAWS.

     THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO A
     STOCKHOLDERS AGREEMENT AMONG THE COMPANY AND THE ORIGINAL PURCHASERS OF THE
     SECURITIES REPRESENTED HEREBY. TRANSFEREES OF SUCH SECURITIES SHOULD REVIEW
     SUCH AGREEMENT TO DETERMINE THEIR RIGHTS AND OBLIGATIONS.



                           --------------------------

                                                      Date: January 28, 2000


                              WARRANT TO PURCHASE
                      5,103,780 SHARES OF COMMON STOCK OF
                          OUTBOARD MARINE CORPORATION


                   Void after 5:00 P.M. (Eastern Time) on the
                      Expiration Date (as defined herein)


     THIS CERTIFIES that QUANTUM INDUSTRIAL PARTNERS LDC (the "Warrant Holder"),
or registered assigns, is entitled to purchase from OUTBOARD MARINE CORPORATION
(the "Company"), a Delaware corporation, at any time after the date hereof and
until 5:00 P.M. (Eastern Time) on the Expiration Date, FIVE MILLION, ONE HUNDRED
THREE THOUSAND, SEVEN HUNDRED EIGHTY fully paid and nonassessable shares of
Common Stock of the Company, $.01 par value per share (the "Common Stock"), at a
purchase price of $.01 per share, in each case subject to adjustment as provided
in Section 6 hereof.

          1.  Definitions.  For the purpose of this Warrant:
              -----------
<PAGE>

               (a)   "Expiration Date" shall mean January 28, 2010.
                      ---------------

               (b)   "Warrant Price" shall mean the price per share at which
                      -------------
shares of Common Stock of the Company are purchasable hereunder, as such price
may be adjusted from time to time hereunder.

               (c)   "Warrant Shares" shall mean the Common Stock purchased upon
                      --------------
exercise of Warrants.

               (d)   "Warrants" shall mean this original Warrant to purchase
                      --------
Common Stock of the Company and any and all Warrants which are issued in
exchange or substitution for the Warrant pursuant to the terms of this Warrant.

          2.  Method of Exercise of Warrants.  This Warrant may be exercised at
              ------------------------------
any time and from time to time after the date hereof and prior to 5:00 P.M.
(Eastern Time) on the Expiration Date, in whole or in part (but not as to
fractional shares), by the surrender of the Warrant, manually or by facsimile
transmission, with the Purchase Agreement attached hereto as Exhibit A properly
                                                             ---------
completed and duly executed, at the principal office of the Company at the
address set forth in Section 10(ii) hereof, or such other location which shall
at that time be the principal office of the Company (the "Principal Office"),
                                                          ----------------
and upon payment to it by certified check or bank draft or wire transfer of
immediately available funds to the order of the Company of the purchase price
for the shares to be purchased upon such exercise.  The person entitled to the
shares so purchased shall be treated for all purposes as the holder of such
shares as of the close of business on the date of exercise and certificates for
the shares of stock so purchased shall be delivered to the person so entitled
within a reasonable time, not exceeding thirty (30) days, after such exercise.
Unless this Warrant has expired, a new Warrant of like tenor and for such number
of shares as the holder of this Warrant shall direct, representing in the
aggregate the right to purchase a number of shares with respect to which this
Warrant shall not have been exercised, shall also be issued to the holder of
this Warrant within such time.

          3.   Conversion Right.
               ----------------

               (a)   In lieu of the payment of the Exercise Price, the Warrant
Holder shall have the right (but not the obligation), to require the Company to
convert this Warrant, in whole or in part, into shares of Common Stock (the
"Conversion Right") as provided for in this Section 3. Upon exercise of the
 ----------------
Conversion Right, the Company shall deliver to the Warrant Holder (without
payment by the Warrant Holder of any of the Warrant Price) in accordance with
Section 2 that number of shares of Common Stock equal to the quotient obtained
by dividing (i) the value of the Warrant at the time the Conversion Right is
exercised (determined by subtracting the aggregate Warrant Price in effect
immediately prior to the exercise of the Conversion Right from the aggregate
Current Market Price (as defined herein) for the shares of Common Stock issuable
upon exercise of the Warrant immediately prior to the exercise of the Conversion
Right) by (ii) the Current Market Price of one share of Common Stock immediately
prior to the exercise of the Conversion Right.

                                       2
<PAGE>

               (b)   The Conversion Right may be exercised by the Warrant Holder
at any time and from time to time prior to 5:00 p.m. (Eastern Time) on the
Expiration Date by surrender of the Warrant, together with notice of such
exercise, to the Company, and specifying the total number of shares of Common
Stock that the Warrant Holder will be issued pursuant to such conversion.

               (c)   Current Market Price of a share of Common Stock as of a
particular date (the "Determination Date") shall mean the average closing price
                      ------------------
of the Company's Common Stock on the principal securities exchange or market on
which such shares are then traded for the last thirty (30) trading days prior to
the Determination Date, or if the Common Stock is not traded on any such
principal securities exchange or market at the time the Conversion Right is
exercised, a market price per share determined in good faith by the Board of
Directors of the Company or, if such determination is not satisfactory to the
Warrant Holder, by a nationally recognized investment banking firm selected by
the Company and the Warrant Holder, the expenses for which shall be borne
equally by the Company and the Warrant Holder.

          4.   Exchange. This Warrant is exchangeable, upon the surrender hereof
               --------
by the holder hereof at the Principal Office of the Company, for new Warrants of
like tenor registered in such holder's name and representing in the aggregate
the right to purchase the number of shares purchasable under the Warrant being
exchanged, each of such new Warrants to represent the right to subscribe for and
purchase such number of shares as shall be designated by said holder at the time
of such surrender.

          5.   Transfer. Any transfer or assignment of this Warrant, whether in
               --------
whole or in part without, must be made in compliance with all applicable federal
and state securities laws and the Company shall not be required to give effect
to any such purported transfer or assignment unless it is reasonably satisfied
that such transfer has been made in compliance with all applicable federal and
state securities laws.  Subject to the immediately preceding sentence, this
Warrant is transferable, in whole or in part, at the Principal Office of the
Company by the holder hereof, in person or by duly authorized attorney, upon
presentation of this Warrant, properly endorsed, for transfer.  Each holder of
this Warrant, by holding it, agrees that the Warrant, when endorsed in blank,
may be deemed negotiable, and that the holder hereof, when the Warrant shall
have been so endorsed, may be treated by the Company and all other persons
dealing with the Warrant as the absolute owner hereof for any purpose and as the
person entitled to exercise the rights represented by the Warrant, or to the
transfer thereof on the books of the Company, any notice to the contrary
notwithstanding.

          6.   Certain Covenants of the Company.  The Company covenants and
               --------------------------------
agrees that all shares which may be issued upon the exercise of this Warrant
will, upon issuance, be duly authorized and validly issued, fully paid and
nonassessable.  The Company covenants and agrees that none of the shares which
may be issued upon the exercise of this Warrant will, upon issuance, be in
violation of or subject to any preemptive rights of any person.  The Company
further covenants and agrees that during the period within which the rights
represented by this Warrant may be exercised, the Company will at all times have
authorized, and reserved for the purpose of

                                       3
<PAGE>

issue upon exercise of the purchase rights evidenced by this Warrant, a
sufficient number of shares of its Common Stock to provide for the exercise of
the rights represented by this Warrant.


          7.   Adjustment of Warrant Price and Number of Shares.  The number and
               ------------------------------------------------
kind of securities purchasable upon the exercise of the Warrants and the Warrant
Price shall be subject to adjustment from time to time upon the happening of
certain events as follows:

               (a)  Reclassification, Consolidation or Merger. At any time while
                    -----------------------------------------
the Warrants remain outstanding and unexpired, in case of any reclassification
or change of outstanding securities issuable upon exercise of the Warrants
(other than a change in par value, or from par value to no par value, or from no
par value to par value or as a result of a subdivision or combination of
outstanding securities issuable upon the exercise of the Warrants) or in case of
any consolidation or merger of the Company with or into another corporation
(other than a merger with another corporation in which the Company is a
continuing corporation and which does not result in any reclassification or
change of rights of outstanding securities issuable upon exercise of the
Warrants, other than a change in par value, or from par value to no par value,
or from no par value to par value, or as a result of a subdivision or
combination of outstanding securities issuable upon exercise of the Warrants),
the Company, or such successor corporation, as the case may be, shall, without
payment of any additional consideration therefor, execute new Warrants providing
that the holders of the Warrants shall have the right to exercise such new
Warrants (upon terms not less favorable to the holders than those then
applicable to the Warrants) and to receive upon such exercise, in lieu of each
share of Common Stock or other security theretofore issuable upon exercise of
the Warrants, the kind and amount of shares of stock, other securities, money or
property receivable upon such reclassification, change, consolidation or merger
by the holder of one share of Common Stock or other security issuable upon
exercise of the Warrants had the Warrants been exercised immediately prior to
such reclassification, change, consolidation or merger. Such new Warrants shall
provide for adjustments which shall be as nearly equivalent as may be
practicable to the adjustments provided for in this Section 7. The provisions of
this subsection 7(a) shall similarly apply to successive reclassifications,
changes, consolidations and mergers.

               (b)  Subdivision or Combination of Shares. If the Company at any
                    ------------------------------------
time while the Warrants remain outstanding and unexpired shall subdivide or
combine its Common Stock, (i) the Warrant Price shall be proportionately
reduced, and the number of shares of Common Stock for which this Warrant may be
exercised shall be proportionately increased, in case of subdivision of such
shares, as of the effective date of such subdivision, or, if the Company shall
take a record of holders of its Common Stock for the purpose of so subdividing,
as of such record date, whichever is earlier, or (ii) the Warrant Price shall be
proportionately increased, and the number of shares of Common Stock for which
this Warrant may be exercised shall be proportionately reduced, in the case of
combination of such shares, as of the effective date of such combination, or, if
the Company shall take a record of holders of its Common Stock for the purpose
of so combining, as of such record date, whichever is earlier.

                                       4
<PAGE>

          (c)  Stock Dividends.  If the Company at any time while the Warrants
               ---------------
remain outstanding and unexpired shall pay a dividend in shares of its Common
Stock, or make other distribution to the holders of Common Stock or of options,
warrants or rights to subscribe for or purchase shares of Common Stock or of
evidences of indebtedness issued by the Company or any other person, then the
Warrant Price shall be adjusted, as of the date the Company shall take a record
of the holders of its Common Stock for the purpose of receiving such dividend or
other distribution (or if no such record is taken, as at the date of such
payment or other distribution), to that price determined by multiplying the
Warrant Price in effect immediately prior to such payment or other distribution
by a fraction (i) the numerator of which shall be the total number of shares of
Common Stock outstanding immediately prior to such dividend or distribution, and
(ii) the denominator of which shall be the total number of shares of Common
Stock outstanding immediately after such dividend or distribution (the
"Fraction"), and the number of shares of Common Stock issuable upon exercise of
this Warrant shall be adjusted by multiplying such number by the reciprocal of
the Fraction.  The number of shares of Common Stock at any time outstanding
shall not include any shares thereof then directly or indirectly owned or held
by or for the account of the Company or any wholly-owned subsidiary.  The
provisions of this subsection 6(c) shall not apply under any of the
circumstances for which an adjustment is provided in subsections 6(a) or 6(b).

          (d)  Liquidating Dividends, Etc.  If the Company at any time while the
               --------------------------
Warrants remain outstanding and unexpired makes a distribution of its assets to
the holders of its Common Stock as a dividend in liquidation or by way of return
of capital or other than as a dividend payable out of earnings or surplus
legally available for dividends under applicable law or any distribution to such
holders made in respect of the sale of all or substantially all of the Company's
assets (other than under the circumstances provided for in the foregoing
subsections 7(a) through 7(c)), the Warrant Holder shall be entitled to receive
upon the exercise hereof, in addition to the shares of Common Stock receivable
upon such exercise, and without payment of any consideration other than the
Warrant Price, an amount of such assets so distributed equal to the value of
such distribution per share of Common Stock multiplied by the number of shares
of Common Stock which, on the record date for such distribution, are issuable
upon exercise of this Warrant (with no further adjustment being made following
any event which causes a subsequent adjustment in the number of shares of Common
Stock issuable upon the exercise hereof), and an appropriate provision therefor
shall be made a part of any such distribution.  The value of a distribution
which is paid in other than cash shall be determined by 75% of the members of
the Board of Directors of the Company, or if 75% of the members of the Board of
Directors are unable to agree upon the value of such consideration, the value
thereof shall be determined by an independent investment bank of nationally
recognized stature that is selected by 75% of the members of the Board of
Directors.

          (e)  Notice of Adjustments.  Whenever the Warrant Price or the number
               ---------------------
of shares of Common Stock purchasable under the terms of this Warrant at the
Warrant Price shall be adjusted pursuant to this Section 6, the Company shall
promptly prepare a certificate signed by its President or a Vice President and
by its Treasurer or Assistant Treasurer or its Secretary or Assistant Secretary,
setting forth in reasonable detail the event requiring the adjustment, the
amount of the adjustment, the method by which such adjustment was calculated
(including a

                                       5
<PAGE>

description of the basis on which the Company's Board of Directors made any
determination hereunder), and the Warrant Price and number of shares of Common
Stock purchasable at that Warrant Price after giving effect to such adjustment,
and shall promptly cause copies of such certificate to be mailed (by first class
and postage prepaid) to the registered holder of this Warrant.

          8.   Fractional Shares.  No fractional shares of the Company's Common
               -----------------
Stock will be issued in connection with any purchase hereunder but in lieu of
such fractional shares, the Company shall make a cash refund therefor equal in
amount to the product of the applicable fraction multiplied by the Warrant Price
paid by the holder for its Warrant Shares upon such exercise.

          9.   Loss, Theft, Destruction or Mutilation.  Upon receipt by the
               --------------------------------------
Company of evidence reasonably satisfactory to it that any Warrant has been
mutilated, destroyed, lost or stolen, and in the case of any destroyed, lost or
stolen Warrant, a bond of indemnity reasonably satisfactory to the Company, or
in the case of a mutilated Warrant, upon surrender and cancellation thereof, the
Company will execute and deliver in the Warrant Holder's name, in exchange and
substitution for the Warrant so mutilated, destroyed, lost or stolen, a new
Warrant of like tenor substantially in the form thereof with appropriate
insertions and variations.

          10.  Notices.  All notices, demands and other communications provided
               --------
for or permitted hereunder shall be made in writing and shall be by registered
or certified first class mail, return receipt requested, telecopier, courier
service, overnight mail or personal delivery:

               (i)  if  to the Warrant Holder:

                    Quantum Industrial Partners LDC
                    Kaya Flamboyan 9
                    Willemstad
                    Curacao
                    Netherlands-Antilles

                    with a copy to:

                    Soros Fund Management LLC
                    888 Seventh Avenue
                    New York, NY 10016
                    Telecopy:  (212) 664-0544
                    Attention:  Michael Neus, Esq.

                    and a copy to:

                    Paul, Weiss, Rifkind, Wharton & Garrison
                    1285 Avenue of the Americas
                    New York, New York 10019-6064
                    Telecopy:  (212) 757-3990

                                       6
<PAGE>

                    Attention:  Richard S. Borisoff, Esq.


               (ii) if to the Company, to the attention of each of its Treasurer
                    and General Counsel at:

                    Outboard Marine Corporation
                    100 Sea-Horse Drive
                    Waukegan, IL 60085
                    Telecopy: (847) 689-6246

                    with a copy to:

                    Davis, Polk & Wardwell
                    450 Lexington Avenue
                    New York, NY 10017
                    Telecopy: (212) 450-4800
                    Attention: Julia K. Cowles, Esq.

          All such notices and communications shall be deemed to have been duly
given when hand delivered by hand, if personally delivered; when delivered by
courier or overnight mail, if delivered by commercial courier service or
overnight mail; five (5) business days after being deposited in the mail,
postage prepaid, if mailed; and when receipt is mechanically acknowledged, if
telecopied.  Any party may by notice given in accordance with this Section 10
designate another address or person for receipt of notices hereunder.

          11.  Headings.  The descriptive headings of the several sections of
               --------
this Warrant are inserted for convenience only and do not constitute a part of
this Warrant.

          12.  Payment of Taxes.  The issuance of certificates for Warrant
               ----------------
Shares shall be made without charge to the Warrant Holder for any stock transfer
or other issuance tax in respect thereto; provided, however, that the Warrant
                                          --------  -------
Holder shall be required to pay any and all taxes that may be payable in respect
of any transfer involved in the issuance and delivery of any certificate in a
name other than that of the then Warrant Holder as upon the books of the
Company.

          13.  Binding Effect; Benefits.  This Warrant shall inure to the
               ------------------------
benefit of and shall be binding upon the Company and the Warrant Holder and
their respective successors and assigns.  Nothing in this Warrant, expressed or
implied, is intended to or shall confer on any person other than the Company and
the Warrant Holder, or their respective successors or assigns, any rights,
remedies, obligations or liabilities under or by reason of this Warrant.

          14.  Severability.  Any term or provision of this Warrant which is
               ------------
invalid or unenforceable in any jurisdiction shall, as to such jurisdiction, be
ineffective to the extent of such

                                       7
<PAGE>

invalidity or unenforceability without rendering invalid or unenforceable the
terms and provisions of this Warrant or affecting the validity or enforceability
of any of the terms or provisions of this Warrant in any other jurisdiction.

          15.  Governing Law.  THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED
               -------------
IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, WITHOUT REGARD TO THE
CONFLICTS OF LAW PRINCIPLES THEREOF.

          16.  No Rights or Liabilities as Stockholders.  No Warrant Holder
               ----------------------------------------
shall, as such, be entitled to vote or to receive dividends or be deemed the
holder of Common Stock that may at any time be issuable upon exercise of this
Warrant for any purpose whatsoever, nor shall anything contained herein be
construed to confer upon the Warrant Holder, as such, any of the rights of a
stockholder of the Company or any right to vote for the election of directors or
upon any matter submitted to stockholders at any meeting thereof, or to give or
withhold consent to any corporate action (whether upon any recapitalization,
issue or reclassification of stock, change of par value or change of stock to no
par value, consolidation, merger or conveyance or otherwise), or to receive
notice of meetings, or to receive dividends or subscription rights, until such
Warrant Holder shall have exercised this Warrant and been issued Common Stock in
accordance with the provisions hereof.  Nothing contained in this Warrant shall
be determined as imposing any liabilities on the Warrant Holder to purchase any
securities, whether such liabilities are asserted by the Company or by creditors
or stockholders of the Company or otherwise.

          17.  Compliance with Securities Laws.
               -------------------------------

               (a)  The Warrant Holder, by acceptance hereof, acknowledges that
this Warrant and the shares of Common Stock to be issued upon exercise hereof
are being acquired solely for the Warrant Holder's own account and not as a
nominee for any other party, and for investment, and that the Warrant Holder
will not offer, sell or otherwise dispose of this Warrant or any shares of
Common Stock to be issued upon exercise hereof except under circumstances that
will not result in a violation of the Securities Act or any state securities
laws. Upon exercise of this Warrant, the Warrant Holder shall, if requested by
the Company, confirm in writing, in a form satisfactory to the Company, that the
shares of Common Stock so purchased are being acquired solely for the Warrant
Holder's own account and not as a nominee for any other party, for investment,
and not with a view toward distribution or resale.

               (b)  This warrant and all shares of Common Stock issued upon
exercise hereof shall be stamped or imprinted with a legend in substantially the
following form (in addition to any legend required by state securities laws):

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE OR RECEIVABLE UPON THE
     EXERCISE OR CONVERSION THEREOF OR AS A RESULT OF THE OWNERSHIP HEREOF  HAVE
     NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
     "ACT"), OR THE SECURITIES LAWS OF ANY STATE.  THE SECURITIES MAY NOT BE
     TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION

                                       8
<PAGE>

     STATEMENT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR PURSUANT
     TO AN APPLICABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF SUCH ACT
     AND SUCH LAWS."

     "THE SECURITIES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO A
     STOCKHOLDERS AGREEMENT AMONG THE COMPANY AND THE ORIGINAL PURCHASERS OF THE
     SECURITIES REPRESENTED HEREBY.  TRANSFEREES OF SUCH SECURITIES SHOULD
     REVIEW SUCH AGREEMENT TO DETERMINE THEIR RIGHTS AND OBLIGATIONS."

          18.  Market Stand-Off Agreement.  Each holder of this Warrant or any
               --------------------------
portion hereof hereby agrees that, during the period of duration specified by
the Company and, in the case of an underwritten public offering, an underwriter
of Common Stock or other securities of the Company, following the effective date
of a registration statement of the Company filed under the Act, it shall not, to
the extent requested by the Company and such underwriter, directly or indirectly
sell, offer to sell, contract to sell (including, without limitation, any short
sale, grant any option to purchase or otherwise transfer or dispose of (other
than to donees who agree to be similarly bound) all or any portion of this
Warrant or shares of Common Stock issued or issuable upon exercise of the
Warrant held by it at any time during such period except common stock included
in such registration; provided, however, that such market stand-off time period
shall not exceed 180 days in the case of an initial public offering and 90 days
in the case of all other offerings.

          In order to enforce the foregoing covenant, the Company may impose
stop-transfer instruction with respect to the foregoing restriction until the
end of such period.

                                       9
<PAGE>

          IN WITNESS WHEREOF, the Company has caused this Warrant to be signed
by its duly authorized officer on the date of this Warrant.


                              OUTBOARD MARINE CORPORATION


                              By:________________________________

                                       10