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                                                                    EXHIBIT 10.1

                                                                  August 4, 2004

Zafiris G. Zafirellis
President and Chief Executive Officer
Biopure Corporation
11 Hurley Street
Cambridge, MA  02141

Dear Zaf:

This letter represents our understanding of the basis upon which C.E. Unterberg,
Towbin LLC, a Delaware limited liability company ("CEUT"), is engaged to provide
financial advisory and investment banking services to Biopure Corporation (the
"Company"). This letter solely relates to such financial advisory and investment
banking services and not to any potential investment in the Company by CEUT or
any of its affiliates.

1.    The Company hereby retains CEUT to act as its exclusive financial advisor
      with respect to a best efforts public offering intended to raise up to
      $18.5 million (including the exercise price of warrants) through sales of
      the Company's common stock and warrants to acquire additional shares of
      the Company's common stock (the "Securities") in a take-down from the
      Company's shelf registration statement. The Company will not offer any of
      the Securities for sale to, or solicit any offers to buy from, any person
      or persons, whether directly or indirectly, otherwise than through CEUT;
      provided, however, that under no circumstances shall CEUT be liable for
      failure to obtain or produce the proposed financing.

2.    As part of our engagement, CEUT will provide the Company with the
      following services:

      a.    Review the Company's current business plan and financial needs, and
            assist in the preparation of a preliminary and final prospectus
            supplement for distribution to prospective investors;

      b.    Identify and contact potential institutional and/or strategic
            investors and assist the Company in conducting a "road show" with
            respect to the public offering;

      c.    As appropriate, with management of the Company, meet with potential
            investors and discuss with them the Company's business; and

      d.    Assist the Company and the Company's legal counsel in preparing
            documents related to the transaction and having such documents
            executed in order to close the transaction and any other agreements
            as may be necessary.

3.    As compensation for the services rendered by CEUT hereunder, the Company
      agrees to pay CEUT at closing for the sale of Securities, a cash fee equal
      to 6.5% of the gross proceeds from the sale of the Securities, together
      with common stock warrants (the "Warrants") equal to 3.0% of the number of
      common shares sold in the transaction. The Warrants will expire on the
      fifth anniversary from closing.

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9Mr. Zafirellis
Page 2 of 4
August 4, 2004

4.    In addition to the fee specified in Section 3 above, the Company shall
      reimburse CEUT for its reasonable expenses including fees and
      disbursements of counsel incurred by CEUT in connection with its
      engagement hereunder.

5.    CEUT and the Company have entered into a separate letter agreement, dated
      the date hereof, providing for the indemnification of CEUT by the Company
      in connection with CEUT's engagement hereunder, the terms of which are
      incorporated into this agreement in their entirety.

6.    For a period of 6 months from the date hereof, the Company grants to CEUT
      the right to provide investment banking services to the Company on an
      exclusive basis in all matters for which investment banking services are
      sought by the Company (the "Right of First Refusal"). For the purposes
      hereof, investment banking services shall consist of (i) acting as lead
      manager for any underwritten public offering of securities of the Company;
      (ii) acting as placement agent or financial advisor in connection with any
      private offering of securities of the Company; and, (iii) acting as
      financial advisor in connection with any sale or other transfer by the
      Company, directly or indirectly, of a majority or controlling portion of
      its capital stock or assets to another entity, any purchase or other
      transfer by another entity, directly or indirectly, of a majority or
      controlling portion of the capital stock or assets of the Company, and any
      merger or consolidation of the Company with another entity, but not
      including strategic alliance transactions. CEUT shall notify the Company
      of its intention to exercise the Right of First Refusal within 10 business
      days following notice in writing by the Company to CEUT of any transaction
      specified in (i)-(iii) above. If CEUT declines to serve as investment
      banker to the Company pursuant to the Right of First Refusal, the Company
      shall have the right to retain any other person or persons to provide such
      services on terms and conditions that are not materially more favorable to
      such other person or persons than the terms declined by CEUT.
      Additionally, during the same 6 month time period, the Company shall pay
      CEUT fees as outlined in paragraph 3 above for any subsequent financing
      with the same investors, introduced to the Company for the first time by
      CEUT, that participate in a transaction contemplated by Section 1 above.

7.    The Company recognizes and confirms that CEUT in acting pursuant to this
      engagement will be using publicly available information and information in
      reports and other materials provided by others, including, without
      limitation, information provided by or on behalf of the Company and that
      CEUT does not assume responsibility for and may rely, without independent
      verification, on the accuracy and completeness of any such information.
      The Company agrees to furnish or cause to be furnished to CEUT all
      necessary or appropriate information for use in its engagement and hereby
      warrants that any information relating to the Company, that is furnished
      to CEUT by or on behalf of the Company, will be true and correct in all
      material respects and not misleading in any material respect.

8.    The term of this engagement shall extend until six (6) months from the
      date of this agreement, unless terminated in writing by either party with
      seven (7) days prior notice. Any such termination shall not (except as
      provided herein) affect the compensation, reimbursement, right of first
      refusal or indemnification provisions set forth herein, all of which shall
      remain in full force and effect. In addition, the Company shall be
      responsible for any fees as outlined above for any financing transaction
      undertaken by the Company in lieu of the contemplated transaction
      described herein with any investors contacted by

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9Mr. Zafirellis
Page 3 of 4
August 4, 2004

      CEUT that is concluded within six (6) months of the date of termination of
      this agreement.

9.    Notwithstanding its engagement hereunder, CEUT may not, without its prior
      written consent, be quoted or referred to in any document, release or
      communication prepared, issued or transmitted by the Company (including
      any entity controlled by, or under common control with, the Company and
      any director, officer, employee or agent thereof).

10.   Following completion of this engagement, CEUT shall have the right to
      place advertisements in financial and other newspapers and journals at its
      own expense describing its services to the Company hereunder.

11.   This Agreement shall be governed by, and construed and enforced in
      accordance with, the laws of the State of New York, without regard to such
      state's rules concerning conflicts of law, and will be binding upon and
      inure to the benefit of the Company and CEUT and their respective
      successors and assigns. Each of the parties hereto also hereby submits to
      the jurisdiction of the federal courts located in the Southern District of
      New York or in any New York State court located in New York County in any
      proceeding arising out of or relating to this Agreement, agrees not to
      commence any suit, action or proceeding relating hereto except in such
      courts, and waives, to the fullest extent permitted by law, the right to
      move to dismiss or transfer any action brought in such court on the basis
      of any objection to personal jurisdiction, venue or inconvenient forum.
      Solely, for purposes of enforcing this Agreement, the Company hereby
      consents to personal jurisdiction, service of process and venue in any
      court in which any claim or proceeding that is subject to this Agreement
      is brought against CEUT. THE COMPANY AND CEUT AGREE TO WAIVE TRIAL BY JURY
      IN ANY ACTION, PROCEEDING OR COUNTERCLAIM BROUGHT BY OR ON BEHALF OF
      EITHER PARTY WITH RESPECT TO ANY MATTER WHATSOEVER RELATING TO OR ARISING
      OUT OF ANY ACTUAL OR PROPOSED TRANSACTION OR THE ENGAGEMENT OF OR
      PERFORMANCE BY CEUT HEREUNDER.

12.   This agreement may be executed in counterparts, each of which shall be
      deemed to be an original, but which together shall constitute one and the
      same agreement.

CEUT will act under this Agreement as an independent contractor with obligations
solely to the Company.

The Company acknowledges that CEUT and its affiliates may have and may in the
future have investment banking and other relationships with parties other than
the Company, which parties may have interests with respect to the proposed
public offering. Although CEUT in the course of such other relationships may
acquire information about the proposed public offering, potential purchasers of
the Securities or such other parties, CEUT shall have no obligation to disclose
such information to the Company or to use such information on behalf of the
Company. Furthermore, the Company acknowledges that CEUT may have fiduciary or
other relationships whereby CEUT may exercise voting power over securities of
various persons, which securities may from time to time include securities of
the Company or of potential purchasers of the Securities or others with
interests in respect of the potential public offering. The Company acknowledges
that CEUT may exercise such powers and otherwise perform its functions in
connection with such fiduciary or other relationships without regard to its
relationship to the Company hereunder.

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9Mr. Zafirellis
Page 4 of 4
August 4, 2004

If the foregoing correctly sets forth the understanding and agreement between
CEUT and the Company, please so indicate in the space provided for that purpose
below, together with the enclosed duplicate original, and return one (1) of
these originals to us, whereupon this letter shall constitute a binding
agreement as of the date hereof.

                                               Sincerely,

                                               C.E. Unterberg,Towbin LLC

                                               By: /s/Christine Gallagher
                                                   --------------------------
                                               Name:  Christine Gallagher
                                               Title: Managing Director

Approved and agreed to as of August ___, 2004:

BIOPURE CORPORATION

By: /s/ Zafiris G. Zafirellis
    ---------------------------
Name:  Zafiris G. Zafirellis
Title: President and Chief Executive Officer

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                                                                  August 3, 2004

C.E. Unterberg, Towbin
350 Madison Avenue
New York, NY 10017

Ladies and Gentlemen:

In connection with the engagement (the "Engagement") of C.E. Unterberg, Towbin
LLC, a Delaware limited liability company ("CEUT") to advise and assist Biopure
Corporation (the "Company") in connection with the matters contemplated by
Section 1 of the letter agreement (a "Transaction") dated the date hereof
between CEUT and the Company (the "Letter Agreement"), the Company agrees that
it will indemnify and hold harmless CEUT and its affiliates and their respective
directors, officers, agents, representatives and employees (collectively,
"Representatives") and each other person controlling CEUT or any of CEUT's
affiliates (collectively, the "Indemnified Parties"), to the fullest extent
permitted by law, from and against any and all losses, expenses, claims,
liabilities or proceedings including, but not limited to, reasonable legal fees
and expenses and the costs of enforcing any of the terms hereof (collectively,
"Losses") (i) related to or arising out of (A) oral or written information
provided by the Company and/or its Representatives in connection with a
Transaction, or (B) any other action or failure to act by (1) the Company and/or
its Representatives or (2) by CEUT or any Indemnified Party at the Company's
request or with the Company's consent, or (ii) otherwise related to or arising
out of the Engagement or any Transaction or conduct in connection therewith;
provided that the Company shall have no indemnification obligation hereunder
with respect to Losses arising from the gross negligence or willful misconduct
of any Indemnified Party.

In the event that the foregoing indemnity is unavailable to any Indemnified
Party for any reason, then the Company agrees to contribute to any Losses
related to or arising out of the engagement or any transaction or conduct in
connection therewith as follows. With respect to Losses referred to in clause
(i) of the preceding paragraph, each of the Company and CEUT shall contribute in
such proportion as is appropriate to reflect the relative benefits received by
CEUT, on the one hand, and by the Company, on the other hand, from a
Transaction. With respect to any other Losses, and for Losses referred to in
clause (i) of the preceding paragraph if the allocation provided by the
immediately preceding sentence is unavailable for any reason, each of the
Company and CEUT shall contribute in such proportion as is appropriate to
reflect not only the relative benefits, but also the relative fault of each of
the Company and CEUT in connection with the alleged misstatements, omissions and
actions and other relevant equitable considerations. Benefits received by the
Company in connection with a Transaction shall be deemed to be equal to the
gross cash consideration received by the Company from the sale of securities in
such Transaction, and the benefits received by CEUT shall be deemed to be equal
to the compensation paid to CEUT by the Company in connection with the
Engagement (exclusive of amounts paid for reimbursement of expenses or paid
under this agreement). Relative fault shall be determined by reference to, among
other things, whether any alleged untrue statement or omission relates to
information provided by, or any alleged conduct is engaged in by, the Company
and/or its Representatives, on the one hand, or CEUT, on the other hand. CEUT
and the Company agree that it would not be just and equitable if contribution
were determined by pro rata allocation or by any other method of allocation that
does not take account of the equitable considerations referred to above.
Notwithstanding anything to the contrary above, in no event shall CEUT be
responsible for any amounts in excess of the amount of the compensation actually
paid by the Company to CEUT in connection with the Engagement (exclusive of
amounts paid for reimbursement of expenses or paid under this agreement). No
person or entity guilty of fraudulent misrepresentation (within the meaning of
Section 11(f) of the Securities Act of 1933, as

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amended) shall be entitled to contribution from any person or entity who was not
guilty of such fraudulent misrepresentation.

Promptly after CEUT receives notice of the commencement of any action or other
proceeding in respect of which indemnification or reimbursement may be sought
hereunder, CEUT will notify the Company thereof; but the omission so to notify
the Company shall not relieve the Company from any obligation hereunder. If any
such action or other proceeding shall be brought against any Indemnified Party,
the Company shall, upon written notice given reasonably promptly following
notice to the Company by such Indemnified Party of such action or proceeding, be
entitled to assume the defense thereof at its expense with counsel chosen by the
Company and reasonably satisfactory to such Indemnified Party; provided,
however, that any Indemnified Party may at its own expense retain separate
counsel to participate in such defense. Notwithstanding the foregoing, such
Indemnified Party shall have the right to employ separate counsel at the
Company's expense and to control its own defense of such action or proceeding
if, in the reasonable opinion of counsel to such Indemnified Party, (i) there
are or may be legal defenses available to such Indemnified Party or to other
Indemnified Parties that are different from or additional to those available to
the Company or (ii) a conflict or potential conflict exists between the Company
and such Indemnified Party that would make such separate representation
advisable. The Company agrees that it will not, without the prior written
consent of CEUT, which consent shall not be unreasonably withheld or delayed,
settle or compromise or consent to the entry of any judgment in any pending or
threatened claim, action or proceeding relating to the matters contemplated by
the Engagement or any Transaction (whether or not any Indemnified Party is a
party thereto) unless such settlement, compromise or consent includes an
unconditional release of CEUT and each other Indemnified Party from all
liability arising or that may arise out of such claim, action or proceeding.

The Company further agrees that no Indemnified Party shall have any liability
(whether direct or indirect, in contract or tort or otherwise) to the Company or
any of its affiliates, Representatives, creditors or security holders for or in
connection with the Engagement or any Transaction, except in the case of the
gross negligence or willful misconduct of any Indemnified Party.

The foregoing agreement is in addition to any rights CEUT may have at common law
or otherwise and shall be binding on and inure to the benefit of any successors,
assigns, and personal representatives of the Company and each Indemnified Party.
This agreement shall be governed by, and construed and enforced in accordance
with, the laws of the State of New York, without regard to such state's rules
concerning conflicts of laws. Each of the parties hereto also hereby submits to
the jurisdiction of the federal courts located in the Southern District of New
York or in any New York State court located in New York County in any proceeding
arising out of or relating to this agreement, including federal district courts
located in such state, agrees not to commence any suit, action or proceeding
relating hereto except in such courts, and waives, to the fullest extent
permitted by law, the right to move to dismiss or transfer any action brought in
such court on the basis of any objection to personal jurisdiction, venue or
inconvenient forum. Solely, for purposes of enforcing this agreement, the
Company hereby consents to personal jurisdiction, service of process and venue
in any court in which any claim or proceeding that is subject to this agreement
is brought against CEUT. ANY RIGHT TO TRIAL BY JURY WITH RESPECT TO ANY CLAIM OR
PROCEEDING RELATED TO OR ARISING OUT OF THE ENGAGEMENT, OR ANY TRANSACTION OR
CONDUCT IN CONNECTION THEREWITH OR THIS AGREEMENT IS WAIVED.

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This agreement shall remain in full force and effect notwithstanding the
completion or termination of the engagement.

                                 Very truly yours,

                                 BIOPURE CORPORATION

                                 By: /s/ Zafiris G.Zafirellis
                                     -------------------------
                                 Name:  Zafiris G. Zafirellis
                                 Title: President and Chief Executive Officer

Agreed:

C.E. Unterberg, Towbin LLC

By: /s/ Christine Gallagher
    ----------------------------
Name:  Christine Gallagher
Title: Managing Director

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                                                               September 8, 2004

Zafiris G. Zafirellis
President and Chief Executive Officer
Biopure Corporation
11 Hurley Street
Cambridge, MA  02141

Dear Zaf:

This letter amends the letter dated August 4, 2004 (the "Engagement Letter")
between the parties hereto. Terms defined in the Engagement Letter and not
otherwise defined herein are used herein with the meaning so defined. Effective
as of the date hereof, the Engagement Letter is hereby amended as follows:

Section 6 of the Engagement Letter is amended and restated to read in its
entirety as follows:

      6.    For a period of 6 months from the date hereof, the Company grants to
            CEUT the right to provide investment banking services to the Company
            on an exclusive basis in all matters for which investment banking
            services are sought by the Company (the "Right of First Refusal").
            For the purposes hereof, investment banking services shall consist
            of (i) acting as lead manager for any underwritten public offering
            of securities of the Company; (ii) acting as placement agent or
            financial advisor in connection with any private offering of
            securities of the Company; and, (iii) acting as financial advisor in
            connection with any sale or other transfer by the Company, directly
            or indirectly, of a majority or controlling portion of its capital
            stock or assets to another entity, any purchase or other transfer by
            another entity, directly or indirectly, of a majority or controlling
            portion of the capital stock or assets of the Company, and any
            merger or consolidation of the Company with another entity, but not
            including strategic alliance transactions. CEUT shall notify the
            Company of its intention to exercise the Right of First Refusal
            within 10 business days following notice in writing by the Company
            to CEUT of any transaction specified in (i)-(iii) above.
            Additionally, during the same 6 month time period, the Company shall
            pay CEUT fees as outlined in paragraph 3 above for any subsequent
            financing with the same investors, introduced to the Company for the
            first time by CEUT, that participate in a transaction contemplated
            by Section 1 above.

This agreement may be executed in counterparts, each of which shall be deemed to
be an original, but which together shall constitute one and the same agreement.
This letter shall be governed by, and construed and enforced in accordance with,
the laws of the State of New York, without regard to such state's rules
concerning conflicts of law, and will be binding upon and inure to the benefit
of the Company and CEUT and their respective successors and assigns. Each of the
parties hereto also hereby submits to the jurisdiction of the federal courts
located in the Southern District of New York or in any New York State court
located in New York County in any proceeding arising out of or relating to this
letter, agrees not to commence any suit, action or proceeding relating hereto
except in such courts, and waives, to the fullest extent permitted by law, the
right to move to dismiss or transfer any action brought in such court on the
basis of any objection to personal jurisdiction, venue or inconvenient forum.
Solely, for purposes of enforcing this letter, the Company hereby consents to
personal jurisdiction, service of process and venue in any court in which any
claim or proceeding that is subject to this Agreement is

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brought against CEUT. THE COMPANY AND CEUT AGREE TO WAIVE TRIAL BY JURY IN ANY
ACTION, PROCEEDING OR COUNTERCLAIM BROUGHT BY OR ON BEHALF OF EITHER PARTY WITH
RESPECT TO ANY MATTER WHATSOEVER RELATING TO OR ARISING OUT OF ANY ACTUAL OR
PROPOSED TRANSACTION OR THE ENGAGEMENT OF OR PERFORMANCE BY CEUT HEREUNDER.

The Engagement Letter as amended hereby is confirmed as being in full force and
effect.

If the foregoing correctly sets forth the understanding and agreement between
CEUT and the Company, please so indicate in the space provided for that purpose
below, together with the enclosed duplicate original, and return one (1) of
these originals to us, whereupon this letter shall constitute a binding
agreement as of the date hereof.

                                                   Sincerely,

                                                   C.E. Unterberg,Towbin LLC

                                                   By: /s/ Christine Gallagher
                                                       -----------------------
                                                       Christine Gallagher
                                                       Managing Director

Approved and agreed to as of September 8, 2004:

BIOPURE CORPORATION

By: /s/ Zafiris G. Zafirellis
    -------------------------
     Zafiris G. Zafirellis
     President and Chief Executive Officer