EXHIBIT 10.4

                            CO-SALE RIGHTS AGREEMENT

     This Co-Sale Rights Agreement (this "AGREEMENT") is entered into as of
October 29, 2004 (the "AGREEMENT DATE"), by and among A-Fem Medical Corporation,
a Nevada corporation (the "COMPANY"), Goldman, Sachs & Co., a New York limited
partnership ("GOLDMAN"), and each of the individuals and entities listed on
Schedule A (each, an "INVESTOR").

                                   BACKGROUND

     A.  The  Company,  Goldman and the Investors, have entered into a Stock and
Warrant  Purchase  Agreement  (the  "PURCHASE  AGREEMENT") of even date herewith
pursuant  to  which  Goldman  desires to sell to the Investors and the Investors
desire  to  purchase  from  Goldman  the  Shares (as such term is defined in the
Purchase  Agreement)  and  Warrants  (as  such  term  is defined in the Purchase
Agreement).

     B.  A condition to the obligations under the Purchase Agreement is that the
Company, Goldman and the Investors enter into this Agreement in order to provide
Goldman with certain rights of co-sale with respect to sales of shares of Common
Stock,  par  value  $0.01  per  share,  of  the  Company  ("COMMON  STOCK").

                                    AGREEMENT
     In consideration of the mutual agreements contained in this Agreement, the
parties agree as follows:

1.     CO-SALE RIGHTS.

     1.1     NOTICE OF PROPOSED TRANSFER. At least five business days before an
Investor (a "SELLING HOLDER") may sell or transfer any shares of Common Stock
(the "OFFERED SHARES") into which shares of Series A Convertible Preferred
Stock, par value $0.01 per share, of the Company ("SERIES A STOCK") have been
converted (the "SUBJECT SHARES"), such Selling Holder shall deliver to Goldman
and the Company a written notice (the "TRANSFER NOTICE") stating: (i) the
Selling Holder's bona fide intention to sell or otherwise transfer Offered
Shares; (ii) the name of each proposed purchaser or other transferee (each, a
"PROPOSED TRANSFEREE"); (iii) the number of Offered Shares to be transferred to
each Proposed Transferee; (iv) the bona fide cash price or the value of the
other consideration for which the Selling Holder proposes to transfer the
Offered Shares (the "OFFERED PRICE"); and (v) the anticipated closing of the
sale or transfer of the Subject Shares. Notwithstanding the foregoing, a Selling
Holder is not required to deliver a Transfer Notice pursuant to this Section
1.1, if the proposed transfer is permitted pursuant to Section 1.4.

     1.2     RIGHT TO PARTICIPATE. If a Selling Holder intends to sell any
Offered Shares to a third party, Goldman shall have the right to participate in
any sale to a Proposed Transferee upon the same terms and conditions as set
forth in the Transfer Notice (the "CO-SALE RIGHT"), subject to the terms and
conditions set forth in this Agreement. Goldman may exercise its Co-Sale Right
by delivering to the Selling Holder proposing to sell or transfer Offered
Shares, within five business days after receipt of the Transfer Notice, written
notice of its intention to participate, specifying the number of shares of
Common Stock Goldman desires to sell to the Proposed


                                                        CO-SALE RIGHTS AGREEMENT
                                        1
<PAGE>
Transferee which number shall in no event exceed the product of (x) the quotient
of (a) the number of shares of Common Stock Goldman has acquired and holds as a
result of, or may acquire, upon exercise of the New Warrant (as defined in the
Purchase Agreement) or such other warrant that has been issued to Goldman upon
partial exercise or transfer of the New Warrant divided by (b) the sum of the
                                                ----------
aggregate number of shares of Common Stock then held by the Investors (assuming
full conversion and exercise of all convertible or exercisable securities)
plus the number of shares of Common Stock then held by Goldman (assuming full
----
exercise of the New Warrant or such other warrant that has been issued to
Goldman upon partial transfer or exercise of the New Warrant) multiplied by (y)
                                                              -------------
the number of shares of Common Stock to be acquired by the Proposed Transferee
(the "TRANSFERRED SHARES"), rounded down to the nearest whole number. At the
closing of the purchase and sale of the Transferred Shares, as determined by the
Selling Holder and the Proposed Transferee, Goldman shall deliver to the Selling
Holder or a designated agent one or more certificates representing the number of
shares of Common Stock Goldman elects to sell hereunder, duly endorsed for
transfer to the Proposed Transferee.

     1.3     CONTINUING RIGHTS. The exercise or non-exercise of Goldman's
Co-Sale Rights with respect to a particular sale of Transferred Shares by a
Selling Holder shall not adversely affect Goldman's Co-Sale Rights with respect
to subsequent sales of Subject Shares.

     1.4     PERMITTED TRANSFERS BY SELLING HOLDERS. Goldman shall have no
Co-Sale Rights with respect to: (i) any pledge of Subject Shares made by an
Investor in a bona fide loan transaction with a commercial bank that creates a
mere security interest; (ii) the donative transfer to an Investor's relatives by
blood, marriage or adoption (each a member of the Selling Holder's ("IMMEDIATE
FAMILY"); (iii) the transfer to a trust established by the Selling Holder for
the benefit of one or more members of such Selling Holder's Immediate Family;
(iv) sales or other transfers by an Investor which when aggregated together do
not exceed 1,000,000 Subject Shares; or (v) the transfer of any Subject Shares
in the event of a Complete Change of Control. For purposes of this Agreement the
term "COMPLETE CHANGE OF CONTROL" means a merger of the Company with or into any
entity that is not an affiliate of the Company or the acquisition of all of the
outstanding capital stock by any person or entity that is not an affiliate of
the Company. In addition, nothing in this Agreement shall be construed to waive
any obligations of Goldman under the New Warrant, including without limitation
the conditions and procedures for exercise thereunder.

2.     TERMINATION. This Agreement shall terminate: (i) when Goldman owns less
than 200,000 shares of Common Stock (assuming full exercise of the New Warrant
or such other warrant that has been issued to Goldman upon partial transfer or
exercise of the New Warrant); (ii) the filing by or against the Company of any
petition under the U.S. Bankruptcy Code, or the appointment of any receiver or
trustee over the Company's assets; (iii) immediately prior to the consummation
of a public offering pursuant to a registration statement filed with the
Securities and Exchange Commission of any shares of Common Stock of the Company;
or (iv) immediately prior to the occurrence of a Complete Change of Control.

3.     LEGEND AND TRANSFER RESTRICTIONS. Each Investor agrees that the Company
may instruct its transfer agent to impose transfer restrictions on the Subject
Shares, to enforce the provisions of this Agreement. The certificates evidencing
Subject Shares held by the Investors shall bear, in addition to any other legend
required under federal or applicable state securities


                                                        CO-SALE RIGHTS AGREEMENT
                                        2
<PAGE>
laws, the legend set forth below. The legend shall be removed upon termination
of this Agreement.

     THE SHARES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO CERTAIN CO-SALE
     RIGHTS AS SET FORTH IN A CO-SALE RIGHTS AGREEMENT ENTERED INTO BY THE
     HOLDER OF THESE SHARES, THE COMPANY AND GOLDMAN SACHS & CO. A COPY OF SUCH
     AGREEMENT MAY BE EXAMINED AT THE PRINCIPAL OFFICE OF THE COMPANY.

4.     MISCELLANEOUS.

     4.1     SUCCESSORS AND ASSIGNS. Except as otherwise provided in this
Agreement, the terms and conditions of this Agreement shall inure to the benefit
of and be binding upon the respective permitted successors and assigns of the
parties. Nothing in this Agreement, express or implied, is intended to confer
upon any party other than the parties hereto or their respective successors and
assigns any rights, remedies, obligations, or liabilities under or by reason of
this Agreement, except as expressly provided in this Agreement. The rights of
Goldman hereunder are only assignable by Goldman to affiliates of Goldman. The
assignees of rights or obligations under this Agreement must agree in writing to
be bound by the terms-and conditions of this Agreement.

     4.2     AMENDMENTS OR WAIVERS. This Agreement or any provision hereof may
be amended, waived, discharged or terminated only by a statement in writing
signed by the party against which enforcement of the amendment, waiver,
discharge or termination is sought.

     4.3     Notices, Etc. All notices and other communications required or
permitted hereunder shall be in writing and shall be deemed given and served for
all purposes when personally delivered, three business days after a writing is
deposited in the United States mail, first class postage prepaid, or one
business day after a writing is deposited with a nationally recognized overnight
courier service for overnight delivery, delivery fees prepaid to the address set
forth below, or to such other address as such party shall have specified in a
written notice given to the other parties hereto:

     (a)  if to an Investor, to such Investor's address on file with the
Company,

     (b)  if to the Company:

                         A-Fem Medical Corporation
                         P.O. Box 2900
                         Wilsonville, OR 97070
                         Attention: William Fleming

     (c)  if to Goldman:

                         Goldman, Sachs & Co.
                         85 Broad Street
                         New York, NY 10004
                         Attention: Lance West, Managing Director

          with a copy to:


                                                        CO-SALE RIGHTS AGREEMENT
                                        3
<PAGE>
                         Obsidian Finance Group, LLC
                         PO Box 3510
                         12 River Road
                         Sunriver, OR 97707
                         Attention: Kevin D. Padrick

     4.4     SEVERABILITY. In case any provision of this Agreement shall be
found by a court of law to be invalid, illegal or unenforceable, the validity,
legality and enforceability of the remaining provisions of this Agreement shall
not in any way be affected or impaired thereby.

     4.5     GOVERNING LAW. This Agreement shall be construed in accordance
with, and governed in all respects by, the laws of the State of Oregon, without
giving effect to principles of conflicts of laws.

     4.6     COUNTERPARTS AND FACSIMILE DELIVERY. This Agreement may be executed
in counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument. Any signature page
delivered by facsimile transmission shall be binding to the same extent as an
original signature page, with regard to any agreement subject to the terms
hereof or any amendment thereto. Any party who delivers such a signature page
agrees to later deliver an original counterpart to any party who requests it.

     4.7     TITLES AND SUBTITLES. The titles of the sections and subsections of
this Agreement are for convenience or reference only and are not to be
considered in construing this Agreement.

     4.8     ENTIRE AGREEMENT. This Agreement constitutes the full and entire
understanding and agreement between the parties with regard to the subjects
hereof and they supersede, merge and render void every other prior written or
oral understanding or agreement among or between the parties hereto.

     4.9     INDEPENDENT NATURE OF INVESTORS' OBLIGATIONS AND RIGHTS. The
obligations of each Investor under this Agreement are several and not joint with
the obligations of any other Investor, and no Investor shall be responsible in
any way for the performance of the obligations of any other Investor under this
Agreement. Nothing contained in this Agreement, and no action taken by any
Investor pursuant thereto, shall be deemed to constitute the Investors as a
partnership, an association, a joint venture or any other kind of entity, or
create a presumption that the Investors are in any way acting in concert or as a
group with respect to such obligations or the transactions to be consummated
pursuant to this Agreement. Each Investor shall be entitled to independently
protect and enforce its rights, including the rights arising out of this
Agreement, and it shall not be necessary for any other Investor to be joined as
an additional party in any proceeding for such purpose. Each Investor represents
that it has been represented by its own separate legal counsel in its review and
negotiation of this Agreement. For reasons of administrative convenience only,
the Investors acknowledge and agree that they and their respective counsel have
chosen to communicate with Company and Company's counsel through Bingham
McCutchen LLP ("Bingham"), but neither Bingham nor Company's counsel represent
                -------
any of the Investors with respect to this Agreement and the transactions
contemplated hereby, except that Bingham represents Sherbrooke Partners, LLC and
Mark Capital, LLC.


                                                        CO-SALE RIGHTS AGREEMENT
                                        4
<PAGE>
     The parties have executed this Co-Sale Rights Agreement as of the Agreement
Date.

A-FEM MEDICAL CORPORATION                  GOLDMAN, SACHS & CO.

By:                                        By:
     ---------------------------------         ---------------------------------

Name:                                      Name:
      --------------------------------           -------------------------------

Its:                                       Its:
     ---------------------------------          --------------------------------

SHERBROOKE PARTNERS, LLC                   MARK CAPITAL, LLC

By:                                        By:
    ----------------------------------         ---------------------------------
        Matthew Balk, Managing Member              Evan Levine, Managing Member

--------------------------------------     -------------------------------------
MATTHEW BALK CUST FOR DAVID BALK           MATTHEW BALK GUST FOR DANIEL BALK

--------------------------------------     -------------------------------------
EVAN LEVINE CUST FOR NATHANIEL LEVINE      EVAN LEVINE CUST FOR ALEXANDER LEVINE

--------------------------------------     -------------------------------------
RICHARD MELNICK                            JOAN ROBBINS

--------------------------------------     -------------------------------------
JONATHAN BALK                              ERIC SINGER

--------------------------------------     -------------------------------------
EVAN LEVINE FBO JULIA SELENKO              EVAN LEVINE FBO MAX SELENKO

--------------------------------------     -------------------------------------
EVAN LEVINE FBO KEIRA MEZEI                EVAN LEVINE FBO REECE MEZEI

DAVID AND MARILYN BALK JTWROS              ROBERT J. & SANDRA S. NEBORSKY JTWROS

     ---------------------------------          --------------------------------
     David Balk                                 Robert J. Neborsky

     ---------------------------------          --------------------------------
     Marilyn Balk                               Sandra S. Neborsky

--------------------------------------     -------------------------------------
ETHAN BALK                                 CRAIG PIERSON

--------------------------------------     -------------------------------------
MICHAEL KOOPER                             BRIAN CORDAY

CGA RESOURCES, LLC                         -------------------------------------
                                           MICHAEL LOWE

By:
    ----------------------------------
     Cass Gunther Adelman, Sole Member


SIGNATURE PAGE T
<PAGE>
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<CAPTION>
                                   SCHEDULE A

                              SCHEDULE OF INVESTORS

--------------------------------------------------------------------------
INVESTOR                                          SHARES         WARRANTS
--------------------------------------------------------------------------
<S>                                              <C>             <C>
Mark Capital, LLC                                1,750,000         642,006
--------------------------------------------------------------------------
Sherbrooke Partners, LLC                         1,750,000         462,006
--------------------------------------------------------------------------
CGA Resources, LLC                                 700,000         100,000
--------------------------------------------------------------------------
Richard Melnick                                    375,000               0
--------------------------------------------------------------------------
Matthew Balk cust for Daniel Balk                  300,000               0
--------------------------------------------------------------------------
Matthew Balk cust for David Balk                   300,000               0
--------------------------------------------------------------------------
David and Marilyn Balk JTWROS                      275,000               0
--------------------------------------------------------------------------
Jonathan Balk                                      250,000               0
--------------------------------------------------------------------------
Evan Levine cust for Nathaniel Levine              250,000               0
--------------------------------------------------------------------------
Evan Levine cust for Alexander Levine              250,000               0
--------------------------------------------------------------------------
Michael Lowe                                       200,000               0
--------------------------------------------------------------------------
Robert J. & Sandra S. Neborsky JTWROS              200,000               0
--------------------------------------------------------------------------
Brian Corday                                       200,000               0
--------------------------------------------------------------------------
Craig Pierson                                      200,000               0
--------------------------------------------------------------------------
Eric Singer                                        192,135               0
--------------------------------------------------------------------------
Joan Robbins                                       100,000               0
--------------------------------------------------------------------------
Ethan Balk                                         100,000               0
--------------------------------------------------------------------------
Evan Levine FBO Julia Selenko                       25,000               0
--------------------------------------------------------------------------
Evan Levine FBO Max Selenko                         25,000               0
--------------------------------------------------------------------------
Evan Levine FBO Keira Mezei                         25,000               0
--------------------------------------------------------------------------
Evan Levine FBO Reece Mezei                         25,000               0
--------------------------------------------------------------------------

                                                 7,492,135       1,204,012
                                                 =========       =========
</TABLE>