<PAGE>

                                                                   EXHIBIT 4.10
                               Biopure Corporation
                             STOCK PURCHASE WARRANT

                            Dated: February 19, 2004

      This certifies that [__________________] or its permitted transferee (the
"Holder") is entitled to purchase from BIOPURE CORPORATION, a Delaware
corporation (the "Company"), at the price and during the period as hereinafter
specified, [__________] shares, including associated preferred stock purchase
rights under that certain Rights Agreement (the "Rights Agreement") dated as of
as of September 24, 1999 between the Company and American Stock Transfer & Trust
Company, as Rights Agent (such shares collectively with such associated rights,
the "Shares"), of Class A common stock, $0.01 par value per share, of the
Company (the "Common Stock") at an exercise price of $15.00 per share subject to
adjustment as described below (as so adjusted from time to time, the "Exercise
Price"), at any time during the five-year period commencing on the date hereof.

      1. The rights represented by this Stock Purchase Warrant (this "Warrant")
shall be exercisable during the period as follows:

            (a) At any time and from time to time between the Closing Date and
5:00 PM New York City time on the earlier of (i) the fourth anniversary of the
Closing Date and (ii) the Mandatory Exercise Date (the earlier of such dates,
the "Expiration Date") inclusive, the Holder shall have the right to purchase
Shares hereunder at the Exercise Price.

            (b) After the Expiration Date, the Holder shall have no right to
purchase all or any portion of the Shares hereunder.

      2. The rights represented by the this Warrant may be exercised at any time
within the period above specified, in whole or in part, by (i) the surrender of
this Warrant (with the purchase form at the end hereof properly executed) at the
principal executive office of the Company (or such other office or agency of the
Company as it may designate by notice in writing to the Holder at the address of
the Holder appearing on the books of the Company) and (ii) payment to the
Company of the Exercise Price then in effect for the number of Shares specified
in the above-mentioned purchase form together with applicable stock transfer
taxes, if any. This Warrant shall be deemed to have been exercised, in whole or
in part to the extent specified, immediately prior to the close of business on
the date this Warrant is surrendered and payment is made in accordance with the
foregoing provisions of this Section 2 or Section 4, and the person or persons
in whose name or names the certificates for the Shares shall be issuable upon
such exercise shall become the holder or holders of record of such Shares at
that time and date. The Shares and the certificates for the Shares so purchased
shall be delivered to the Holder within a reasonable time, not exceeding ten
Business Days (as defined below), after the rights represented by this Warrant
shall have been so exercised.

      3. Any transfer of this Warrant shall be effected by the Holder by (i)
executing the form of assignment at the end hereof and (ii) surrendering this
Warrant for cancellation at the office or agency of the Company referred to in
Section 2 hereof, accompanied by a written instrument of transfer in form
reasonably satisfactory to the Company, duly executed by the registered Holder
thereof or by the duly appointed legal representative thereof or by a duly
authorized attorney-in-fact. Upon any transfer of this Warrant or any part
thereof in accordance with the first sentence of this Section 3(a), the Company
shall issue, in the name or names specified by the Holder (including the
Holder), a new Warrant or Warrants of like tenor and representing in the
aggregate rights to purchase the same number of Shares as are purchasable
hereunder at such time. No transfer of this Warrant shall be made in the records
of the Company from and after the date that the Company gives a Mandatory
Exercise Notice pursuant to Section 4.

      4. On any Notification Date (as defined below), the Company may deliver a
written notice to the Holder at the address of the Holder appearing on the books
of the Company (the "Mandatory Exercise

<PAGE>

Notice"). The Mandatory Exercise Notice shall set forth the Closing Price of a
share of Common Stock on each of the ten consecutive Trading Days immediately
preceding the date of the Mandatory Exercise Notice and shall state that this
Warrant must be exercised in conformity with Section 2 on or before a date
specified in the Mandatory Exercise Notice (the "Mandatory Exercise Date"),
which shall be at least twenty Business Days after the date of mailing of the
Mandatory Exercise Notice. If the Holder does not exercise this Warrant in full
on or before the Mandatory Exercise Date, then (i) the Holder shall forfeit such
Holder's rights, title and interest under this Warrant or portion thereof not
exercised, (ii) this Warrant or portion thereof not exercised shall be deemed
terminated, and (iii) the Company may treat this Warrant or portion thereof not
exercised as void for all purposes. "Notification Date" shall mean any Business
Day after February 19, 2006 which is immediately preceded by ten consecutive
Trading Days on each of which the daily volume weighted average price ("VWAP")
for the Common Stock was greater than 200% of the Exercise Price. "Business Day"
shall mean any day, other than a Saturday or a Sunday or a day on which banking
institutions in the State of New York are authorized or obligated by law,
regulation or order to close. "Trading Day" shall mean any day on which the
principal United States securities exchange or trading market on which the
Common Stock is listed or traded (the "Principal Market") as reported by
Bloomberg Financial Markets is open for trading.

      5. The Company covenants and agrees that all Shares which may be purchased
hereunder will, upon issuance and delivery against payment therefore of the
requisite purchase price, be duly and validly issued, fully paid and
nonassessable. Unless otherwise indicated, the Shares so purchased shall be
delivered to the Holder by the Company, which shall cause its transfer agent to
electronically transmit the Shares so purchased to the Holder by crediting the
account of the holder or its nominee with the Depository Trust Company through
its Deposit Withdrawal Agent Commission system. The Company further covenants
and agrees that, during the period within which this Warrant may be exercised,
the Company will at all times have authorized and reserved a sufficient number
of shares of its Common Stock to provide for the exercise of this Warrant.

      6. This Warrant shall not entitle the Holder to any voting rights or other
rights, including without limitation notice of meetings of other actions or
receipt of dividends, as a stockholder of the Company.

      7. The Exercise Price in effect at the time and the number and kind of
securities purchasable upon the exercise of this Warrant shall be subject to
adjustment from time to time upon the happening of certain events as follows:

            (a) In case the Company shall (i) declare a dividend or make a
distribution on its outstanding shares of Common Stock in shares of Common
Stock, (ii) subdivide or reclassify its outstanding shares of Common Stock into
a greater number of shares, (iii) combine or reclassify its outstanding shares
of Common Stock into a smaller number of shares, or (iv) enter into any
transaction whereby the outstanding shares of Common Stock of the Company are at
any time changed into or exchanged for a different number or kind of shares or
other security of the Company or of another corporation through reorganization,
merger, consolidation, liquidation or recapitalization, then appropriate
adjustments in the number of Shares (or other securities for which such Shares
have previously been exchanged or converted) subject to this Warrant shall be
made and the Exercise Price in effect at the time of the record date for such
dividend or distribution or of the effective date of such subdivision,
combination, reclassification, reorganization, merger, consolidation,
liquidation or recapitalization shall be proportionately adjusted so that the
Holder of this Warrant exercised after such date shall be entitled to receive
the aggregate number and kind of shares of Common Stock which, if this Warrant
had been exercised by such Holder immediately prior to such date, the Holder
would have been entitled to receive upon such dividend, distribution,
subdivision, combination, reclassification, reorganization, merger,
consolidation, liquidation or recapitalization. For example, if the Company
declares a 2 for 1 stock distribution and the Exercise Price hereof immediately
prior to such event was $4.00 per Share and the number of Shares issuable upon
exercise of this Warrant was 10,000, the adjusted Exercise Price immediately
after such event would be $2.00 per Share and the adjusted number of Shares
issuable upon exercise of this Warrant would be 20,000. Such adjustment shall be
made successively whenever any event listed above shall occur.

                                       2
<PAGE>

            (b) In case the Company shall fix a record date for the issuance of
rights or warrants to all holders of its Common Stock entitling them to
subscribe for or purchase shares of Common Stock (or securities convertible into
Common Stock) at a price (the "Subscription Price") (or having a conversion
price per share) less than the current market price per share of Common Stock as
determined pursuant to Section 7(e) on such record date, the Exercise Price
shall be adjusted so that the same shall equal the price determined by
multiplying the same by a fraction, the numerator of which shall be the sum of
the number of shares of Common Stock outstanding on the record date mentioned
below and the number of additional shares of Common Stock which the aggregate
offering price of the total number of shares of Common Stock so offered (or the
aggregate conversion price of the convertible securities so offered) would
purchase at the current market price per share of Common Stock on such record
date, and the denominator of which shall be the sum of the number of shares of
Common Stock outstanding on the record date mentioned below and the number of
additional shares of Common Stock offered for subscription or purchase (or into
which the convertible securities so offered are convertible). Such adjustment
shall be made successively whenever such rights or warrants are issued and shall
become effective immediately after the record date for the determination of
stockholders entitled to receive such rights or warrants; and to the extent that
shares of Common Stock are not delivered (or securities convertible into Common
Stock are not delivered) after the expiration of such rights or warrants the
Exercise Price shall be readjusted to the Exercise Price which would then be in
effect had the adjustments made upon the issuance of such rights or warrants
been made upon the basis of delivery of only the number of shares of Common
Stock (or securities convertible into Common Stock) actually delivered. This
Section 7(b) shall not apply to the occurrence of a "Distribution Date" under
the Rights Agreement.

            (c) In case the Company shall hereafter distribute to all holders of
its Common Stock evidences of its indebtedness or assets (excluding cash
dividends or distributions and dividends or distributions referred to in Section
7(a) above) or subscription rights or warrants (excluding those referred to in
Section 7(b) above), then in each such case the Exercise Price shall be adjusted
by multiplying the same by a fraction, the numerator of which shall be the total
number of shares of Common Stock then outstanding multiplied by the current
market price per share of Common Stock (as defined in Section 7(e) below), less
the fair market value (as determined by the Company's Board of Directors) of
said assets, or evidences of indebtedness so distributed or of such rights or
warrants, and the denominator of which shall be the total number of shares of
Common Stock outstanding multiplied by such current market price per share of
Common Stock. Such adjustment shall be made whenever any such distribution is
made and shall become effective immediately after the record date for the
determination of stockholders entitled to receive such distribution and to the
extent that any subscription rights or warrants are not exercised before the
expiration of such rights or warrants the Exercise Price shall be readjusted to
the Exercise Price which would then be in effect had the adjustments made upon
the issuance of such rights or warrants been made upon the basis of delivery of
only the number of rights or warrants actually exercised. This Section 7(c)
shall not apply to the occurrence of a "Distribution Date" under the Rights
Agreement.

            (d) Whenever the Exercise Price payable upon exercise of this
Warrant is adjusted pursuant to Sections (a), (b) or (c) above, the number of
Shares purchasable upon exercise of this Warrant shall simultaneously be
adjusted by multiplying the number of Shares issuable upon exercise of this
Warrant by the Exercise Price in effect immediately prior to such adjustment and
dividing the product so obtained by the Exercise Price, as adjusted.

            (e) For the purpose of any computation under Subsection (c) above,
the current market price per share of Common Stock at any date shall be deemed
to be the closing price on the Trading Day immediately preceding the date as of
which the current market price is being determined, provided that if the Common
Stock is not then listed on any market or exchange, then the current market
price shall be the average of the closing bid prices for the Common Stock on the
OTC Bulletin Board, or, if such is not available, the Pink Sheets LLC (formerly
the National Quotation Bureau), or otherwise the average of the closing bid
prices for the Common Stock quoted by two market-makers of the Common Stock, or
otherwise such Market Price shall be the fair market value of one share of
Common Stock as reasonably determined in good faith by the Company and the
Holders. "Closing price" shall mean the last sale price for the Common Stock on
the Principal Market on any particular Trading Day.

                                       3
<PAGE>

            (f) No adjustment in the Exercise Price shall be required unless
such adjustment would require an increase or decrease of at least five cents
($0.05) in such price; provided, however, that any adjustments which may by
reason of this Section 7(f) not be required to be made shall be carried forward
and taken into account in any subsequent adjustment required to be made
hereunder. All calculations under this Section 7 shall be made to the nearest
cent or to the nearest one-hundredth of a share, as the case may be. Anything in
this Section 7 to the contrary notwithstanding, the Company shall be entitled,
but shall not be required, to make such changes in the Exercise Price, in
addition to those required by this Section 7, as it shall determine, in its sole
discretion, to be advisable in order that any dividend or distribution in shares
of Common Stock, or any subdivision, reclassification or combination of Common
Stock hereafter made by the Company shall not result in any Federal income tax
liability to the holders of the Common Stock or securities convertible into
Common Stock.

            (g) Whenever the Exercise Price is adjusted, as herein provided, the
Company shall promptly cause a notice setting forth the adjusted Exercise Price
and adjusted number of Shares issuable upon exercise of this Warrant to be
mailed to the Holder, at its address set forth herein, and shall cause a
certified copy thereof to be mailed to the Company's transfer agent, if any. The
Company may retain a firm of independent certified public accountants selected
by the Board of Directors (who may be the regular accountants employed by the
Company) to make any computation required by this Section 7, and a certificate
signed by such firm shall be conclusive evidence of the correctness of such
adjustment.

            (h) In the event that at any time, as a result of an adjustment made
pursuant to the provisions of this Section 7, the Holder of this Warrant
thereafter shall become entitled to receive any shares of the Company other than
Common Stock, thereafter the number of such other shares so receivable upon
exercise of this Warrant shall be subject to adjustment from time to time in a
manner and on terms as nearly equivalent as practicable to the provisions with
respect to the Common Stock contained in Sections 7(a) to (f), inclusive, above.

      8. This Warrant shall be governed by and in accordance with the laws of
the State of Delaware without regard to conflict of laws principles thereof.

      9. In case of any consolidation of the Company with, or merger of the
Company into, any other entity, or in case of any sale or conveyance of all or
substantially all of the assets of the Company other than in connection with a
plan of complete liquidation of the Company at any time prior to the Expiration
Date, then as a condition of such consolidation, merger or sale or conveyance,
the Company shall give written notice of consolidation, merger, sale or
conveyance to the Holder and, from and after the effective date of such
consolidation, merger, sale or conveyance this Warrant shall represent only the
right to receive the consideration that would have been issuable in respect of
the Shares underlying this Warrant in such consolidation, merger, sale or
conveyance had this Warrant been exercised in full immediately prior to such
effective time and the Holder shall have no further rights under this Warrant
other than the right to receive such consideration.

         [The remainder of this page has been intentionally left blank.]

                            [Signature Page Follows]

                                       4
<PAGE>

      IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by
its duly authorized officer under its corporate seal, and this Warrant to be
dated February 19, 2004.

                                         BIOPURE CORPORATION

                                         By: __________________________________
                                             Name: Francis H. Murphy
                                             Title: Chief Financial Officer

                                       5
<PAGE>

                                  PURCHASE FORM

                  (To be signed only upon exercise of Warrant)

      The undersigned, the holder of the foregoing Warrant, hereby irrevocably
elects to exercise the purchase rights represented by such Warrant for, and to
purchase thereunder, _______________ Shares of Class A Common Stock, $0.01 par
value per share (the "Shares"), of BIOPURE CORPORATION and tenders herewith
payment of the aggregate Exercise Price in respect of the Shares in full, in the
amount of $_________; and requests that the certificates for the Shares be
issued in the name(s) of, and delivered to _________________, whose address(es)
is (are):

Dated: _______________, ____

                                                     By: _____________________

                                                     _________________________

                                                     _________________________
                                                     Address

<PAGE>

                                  TRANSFER FORM

                  (To be signed only upon transfer of Warrant)

      For value received, the undersigned hereby sells, assigns, and transfers
unto ____________________ the right to purchase Shares represented by the
foregoing Warrant to the extent of __________ Shares, and appoints
_________________________ attorney to transfer such rights on the books of
Biopure Corporation, with full power of substitution in the premises.

Dated: _______________, ____

                                                     By:______________________

                                                     _________________________

                                                     _________________________
                                                     Address

In the presence of:

_________________________