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                                                                    Exhibit 10.4

THIS WARRANT AND THE SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE OF THIS
WARRANT HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED.
THIS WARRANT AND THE COMMON STOCK ISSUABLE UPON EXERCISE OF THIS WARRANT MAY NOT
BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN
EFFECTIVE REGISTRATION STATEMENT AS TO THIS WARRANT UNDER SAID ACT OR AN OPINION
OF COUNSEL REASONABLY SATISFACTORY TO TRANSGENOMIC, INC. THAT SUCH REGISTRATION
IS NOT REQUIRED.

                              Right to Purchase 550,000 Shares of Common
                              Stock of Transgenomic, Inc. (subject to adjustment
                              as provided herein)

                          COMMON STOCK PURCHASE WARRANT

No. 2003-1                                 Issue Date:  December 3, 2003

          Transgenomic, Inc., a corporation organized under the laws of the
State of Delaware (the "Company"), hereby certifies that, for value received,
LAURUS MASTER FUND, LTD., or assigns (the "Holder"), is entitled, subject to the
terms set forth below, to purchase from the Company from and after the Issue
Date of this Warrant and at any time or from time to time before 5:00 p.m., New
York time, through seven (7) years after such date (the "Expiration Date"), up
to 550,000 fully paid and nonassessable shares of Common Stock (as hereinafter
defined), $.01 par value, of the Company, at the Exercise Price (as defined
below). The number and character of such shares of Common Stock and the Exercise
Price are subject to adjustment as provided herein.

          As used herein the following terms, unless the context otherwise
requires, have the following respective meanings:

          (a)    The term "Company" shall include Transgenomic, Inc. and any
corporation which shall succeed or assume the obligations of Transgenomic, Inc.
hereunder.

          (b)    The term "Common Stock" includes (a) the Company's Common
Stock, par value $.01 per share, and (b) any other securities into which or for
which any of the securities described in (a) may be converted or exchanged
pursuant to a plan of recapitalization, reorganization, merger, sale of assets
or otherwise.

          (c)    The term "Other Securities" refers to any stock (other than
Common Stock) and other securities of the Company or any other person (corporate
or otherwise) which the holder of the Warrant at any time shall be entitled to
receive, or shall have received, on the exercise of the Warrant, in lieu of or
in addition to Common Stock, or which at any time shall be issuable or shall
have been issued in exchange for or in replacement of Common Stock or Other
Securities pursuant to Section 4 or otherwise.

          (d)     The term "Exercise Price" shall be as follows:

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                 a.     200,000 shares at $2.25 per share;

                 b.     200,000 shares at $2.44 per share; and

                 c.     150,000 shares at $2.82 per share.

     2.   EXERCISE OF WARRANT.

          2.1    NUMBER OF SHARES ISSUABLE UPON EXERCISE. From and after the
date hereof through and including the Expiration Date, the Holder shall be
entitled to receive, upon exercise of this Warrant in whole or in part, by
delivery of an original or fax copy of the exercise notice attached hereto as
Exhibit A (the "Exercise Notice"), shares of Common Stock of the Company,
subject to adjustment pursuant to Section 4.

          2.2    FAIR MARKET VALUE. Fair Market Value of a share of Common Stock
as of a particular date (the "Determination Date") shall mean:

          (a)    If the Company's Common Stock is traded on an exchange or is
quoted on the National or SmallCap Market of The Nasdaq Stock Market,
Inc.("Nasdaq"), then the closing or last sale price, respectively, reported for
the last business day immediately preceding the Determination Date.

                 (b)    If the Company's Common Stock is not traded on an
exchange or on the Nasdaq but is traded on the NASD OTC Bulletin Board or BBX
Exchange, then the mean of the average of the closing bid and asked prices
reported for the last business day immediately preceding the Determination Date.

                 (c) Except as provided in clause (d) below, if the Company's
Common Stock is not publicly traded, then as the Holder and the Company agree or
in the absence of agreement by arbitration in accordance with the rules then in
effect of the American Arbitration Association, before a single arbitrator to be
chosen from a panel of persons qualified by education and training to pass on
the matter to be decided.

                 (d) If the Determination Date is the date of a liquidation,
dissolution or winding up, or any event deemed to be a liquidation, dissolution
or winding up pursuant to the Company's charter, then all amounts to be payable
per share to holders of the Common Stock pursuant to the charter in the event of
such liquidation, dissolution or winding up, plus all other amounts to be
payable per share in respect of the Common Stock in liquidation under the
charter, assuming for the purposes of this clause (d) that all of the shares of
Common Stock then issuable upon exercise of the Warrant are outstanding at the
Determination Date.

     3.  PROCEDURE FOR EXERCISE.

          3.1    DELIVERY OF STOCK CERTIFICATES, ETC. ON EXERCISE. The Company
agrees that the shares of Common Stock purchased upon exercise of this Warrant
shall be deemed to be issued to the Holder as the record owner of such shares as
of the close of business on the date on which this Warrant shall have been
surrendered and payment made for such shares as aforesaid. As soon as
practicable after the exercise of this Warrant in full or in part, and in any
event within

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3 business days thereafter, the Company at its expense (including the payment by
it of any applicable issue taxes) will cause to be issued in the name of and
delivered to the Holder, or as such Holder (upon payment by such holder of any
applicable transfer taxes) may direct in compliance with applicable securities
laws, a certificate or certificates for the number of duly and validly issued,
fully paid and nonassessable shares of Common Stock (or Other Securities) to
which such Holder shall be entitled on such exercise, plus, in lieu of any
fractional share to which such holder would otherwise be entitled, cash equal to
such fraction multiplied by the then Fair Market Value of one full share,
together with any other stock or other securities and property (including cash,
where applicable) to which such Holder is entitled upon such exercise pursuant
to Section 1 or otherwise.

          3.2    EXERCISE.

          (a)    Payment may be made either in (i) cash or by certified or
official bank check payable to the order of the Company equal to the applicable
aggregate Exercise Price, (ii) by delivery of the Warrant, Common Stock and/or
Common Stock receivable upon exercise of the Warrant in accordance with Section
(b) below, or (iii) by a combination of any of the foregoing methods, for the
number of Common Shares specified in such form (as such exercise number shall be
adjusted to reflect any adjustment in the total number of shares of Common Stock
issuable to the holder per the terms of this Warrant) and the Holder shall
thereupon be entitled to receive the number of duly authorized, validly issued,
fully-paid and non-assessable shares of Common Stock (or Other Securities)
determined as provided herein.

          (b)    Notwithstanding any provisions herein to the contrary, if the
Fair Market Value of one share of Common Stock is greater than the Exercise
Price (at the date of calculation as set forth below), in lieu of exercising
this Warrant for cash, the Holder may elect to receive shares equal to the value
(as determined below) of this Warrant (or the portion thereof being exercised)
by surrender of this Warrant at the principal office of the Company together
with the properly endorsed Exercise Notice in which event the Company shall
issue to the Holder a number of shares of Common Stock computed using the
following formula:

          X=Y (A-B)
              -----
                A

     Where X =   the number of shares of Common Stock to be issued to the Holder

          Y=     the number of shares of Common Stock purchasable under
                 the Warrant or, if only a portion of the Warrant is
                 being exercised, the portion of the Warrant being
                 exercised (at the date of such calculation)

          A=     the Fair Market Value of one share of the Company's Common
                 Stock (at the date of such calculation)

          B=     Exercise Price (as adjusted to the date of such calculation)

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     4.   EFFECT OF REORGANIZATION, ETC.; ADJUSTMENT OF EXERCISE PRICE.

          4.1    REORGANIZATION, CONSOLIDATION, MERGER, ETC. In case at any time
or from time to time, the Company shall (a) effect a reorganization, (b)
consolidate with or merge into any other person, or (c) transfer all or
substantially all of its properties or assets to any other person under any plan
or arrangement contemplating the dissolution of the Company, then, in each such
case, as a condition to the consummation of such a transaction, proper and
adequate provision shall be made by the Company whereby the Holder of this
Warrant, on the exercise hereof as provided in Section 1 at any time after the
consummation of such reorganization, consolidation or merger or the effective
date of such dissolution, as the case may be, shall receive, in lieu of the
Common Stock (or Other Securities) issuable on such exercise prior to such
consummation or such effective date, the stock and other securities and property
(including cash) to which such Holder would have been entitled upon such
consummation or in connection with such dissolution, as the case may be, if such
Holder had so exercised this Warrant, immediately prior thereto, all subject to
further adjustment thereafter as provided in Section 4.

          4.2    DISSOLUTION. In the event of any dissolution of the Company
following the transfer of all or substantially all of its properties or assets,
the Company, prior to such dissolution, shall at its expense deliver or cause to
be delivered the stock and other securities and property (including cash, where
applicable) receivable by the Holder of the Warrant after the effective date of
such dissolution pursuant to Section 3.1 to a bank or trust company having its
principal office in New York, NY, as trustee for the Holder of the Warrant.

          4.3    CONTINUATION OF TERMS. Upon any reorganization, consolidation,
merger or transfer (and any dissolution following any transfer) referred to in
this Section 4, this Warrant shall continue in full force and effect and the
terms hereof shall be applicable to the shares of stock and other securities and
property receivable on the exercise of this Warrant after the consummation of
such reorganization, consolidation or merger or the effective date of
dissolution following any such transfer, as the case may be, and shall be
binding upon the issuer of any such stock or other securities, including, in the
case of any such transfer, the person acquiring all or substantially all of the
properties or assets of the Company, whether or not such person shall have
expressly assumed the terms of this Warrant as provided in Section 5. In the
event this Warrant does not continue in full force and effect after the
consummation of the transactions described in this Section 4, then only in such
event will the Company's securities and property (including cash, where
applicable) receivable by the holders of the Warrant be delivered to the Trustee
as contemplated by Section 4.2.

     5.  EXTRAORDINARY EVENTS REGARDING COMMON STOCK.

          5.1    RECLASSIFICATION, ETC. If the Company at any time shall, by
reclassification or otherwise, change the Common Stock into the same or a
different number of securities of any class or classes, this Warrant shall
thereafter be deemed to evidence the right to be issued an adjusted number of
such securities and kind of securities as would have been issuable as the result
of such change with respect to the Common Stock immediately prior to such
reclassification or other change.

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          5.2    STOCK SPLITS, COMBINATIONS AND DIVIDENDS. If the shares of
Common Stock are subdivided or combined into a greater or smaller number of
shares of Common Stock, or if a dividend is paid on the Common Stock in shares
of Common Stock, the Exercise Price shall be proportionately reduced in case of
subdivision of shares or stock dividend or proportionately increased in the case
of combination of shares, in each such case by the ratio which the total number
of shares of Common Stock outstanding immediately after such event bears to the
total number of shares of Common Stock outstanding immediately prior to such
event.

          5.3    SHARE ISSUANCES. Subject to the provisions of this Section, if
the Company shall at any time issue any shares of Common Stock to a person other
than the Holder (except (a) pursuant to Sections 5.1 or 5.2 above; (b) pursuant
to options, warrants, or other obligations to issue shares outstanding on the
date hereof as disclosed to Holder in writing; or (c) pursuant to options that
may be issued under any employee incentive stock option and/or any qualified
stock option plan adopted by the Company) for a consideration per share (the
"Offer Price") less than the Exercise Price in effect at the time of such
issuance, then the Exercise Price shall be immediately reset pursuant to the
formula below. For purposes hereof, the issuance of any security of the Company
convertible into or exercisable or exchangeable for Common Stock shall result in
an adjustment to the Exercise Price at the time of issuance of such securities.
If the Company issues any additional shares pursuant to this Section then, and
thereafter successively upon each such issue, the Exercise Price shall be
adjusted by multiplying the then applicable Exercise Price by the following
fraction:

                                      A + B
                          (A + B) + [((C - D) X B) / C]

              A = Actual shares outstanding prior to such offering
                     B = Actual shares sold in the offering
                               C = Exercise Price
                               D = Offering price

          5.4    COMPUTATION OF CONSIDERATION. For purposes of any computation
respecting consideration received pursuant to Section 5.3 above, the following
shall apply:

                 (a)    In the case of the issuance of shares of Common Stock
for cash, the consideration shall be the amount of such cash, provided that in
no case shall any deduction be made for any commissions, discounts or other
expenses incurred by the Company for any underwriting of the issue or otherwise
in connection therewith;

                 (b)    In the case of the issuance of shares of Common Stock
for a consideration in whole or in part other than cash, the consideration other
than cash shall be deemed to be the fair market value thereof as determined in
good faith by the Board of Directors of the Company (irrespective of the
accounting treatment thereof); and

                 (c)    Upon any such exercise, the aggregate consideration
received for such securities shall be deemed to be the consideration received by
the Company for the issuance

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of such securities plus the additional minimum consideration, if any, to be
received by the Company upon the conversion or exchange thereof (the
consideration in each case to be determined in the same manner as provided in
clauses (a) and (b) of this Section 5.4).

     6. In the event that the Company shall (a) issue additional shares of the
Common Stock as a dividend or other distribution on outstanding Common Stock,
(b) subdivide its outstanding shares of Common Stock, (c) combine its
outstanding shares of the Common Stock into a smaller number of shares of the
Common Stock or (d) issue any shares of Common Stock to a Person other than the
Holder (other than (i) pursuant to Subsections (a), (b) or (c) above or (ii)
pursuant to options, warrants or other obligations to issue shares outstanding
on the date hereof or (iii) any shares issued for incentive stock options or
NonQualified stock options in each case under the Company's Employee Stock
Option Plan) for a consideration per share or having an exercise, conversion or
exchange price less than the Exercise Price in effect at the time of such
issuance, then, in each such event, the Exercise Price shall, simultaneously
with the happening of such event, be adjusted by multiplying the then Exercise
Price by a fraction, the numerator of which shall be the number of shares of
Common Stock outstanding immediately prior to such event and the denominator of
which shall be the number of shares of Common Stock outstanding immediately
after such event, and the product so obtained shall thereafter be the Exercise
Price then in effect. The Exercise Price, as so adjusted, shall be readjusted in
the same manner upon the happening of any successive event or events described
herein in this Section 4. The number of shares of Common Stock that the holder
of this Warrant shall thereafter, on the exercise hereof as provided in Section
1, be entitled to receive shall be increased to a number determined by
multiplying the number of shares of Common Stock that would otherwise (but for
the provisions of this Section 4) be issuable on such exercise by a fraction of
which (a) the numerator is the Exercise Price that would otherwise (but for the
provisions of this Section 4) be in effect, and (b) the denominator is the
Exercise Price in effect on the date of such exercise.

     7.   CERTIFICATE AS TO ADJUSTMENTS. In each case of any adjustment or
readjustment in the shares of Common Stock (or Other Securities) issuable on the
exercise of the Warrant, the Company at its expense will promptly cause its
Chief Financial Officer or other appropriate designee to compute such adjustment
or readjustment in accordance with the terms of the Warrant and prepare a
certificate setting forth such adjustment or readjustment and showing in detail
the facts upon which such adjustment or readjustment is based, including a
statement of (a) the consideration received or receivable by the Company for any
additional shares of Common Stock (or Other Securities) issued or sold or deemed
to have been issued or sold, (b) the number of shares of Common Stock (or Other
Securities) outstanding or deemed to be outstanding, and (c) the Exercise Price
and the number of shares of Common Stock to be received upon exercise of this
Warrant, in effect immediately prior to such adjustment or readjustment and as
adjusted or readjusted as provided in this Warrant. The Company will forthwith
mail a copy of each such certificate to the holder of the Warrant and any
Warrant agent of the Company (appointed pursuant to Section 11 hereof).

     8.   RESERVATION OF STOCK, ETC. ISSUABLE ON EXERCISE OF WARRANT. The
Company will at all times reserve and keep available, solely for issuance and
delivery on the exercise of the Warrant, shares of Common Stock (or Other
Securities) from time to time issuable on the exercise of the Warrant.

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     9.   ASSIGNMENT; EXCHANGE OF WARRANT. Subject to compliance with applicable
securities laws, this Warrant, and the rights evidenced hereby, may be
transferred by any registered holder hereof (a "Transferor") with respect to any
or all of the Shares. On the surrender for exchange of this Warrant, with the
Transferor's endorsement in the form of Exhibit B attached hereto (the
"Transferor Endorsement Form") and together with evidence reasonably
satisfactory to the Company demonstrating compliance with applicable securities
laws, which shall include, without limitation, a legal opinion from the
Transferor's counsel that such transfer is exempt from the registration
requirements of applicable securities laws, the Company at its expense) but with
payment by the Transferor of any applicable transfer taxes) will issue and
deliver to or on the order of the Transferor thereof a new Warrant of like
tenor, in the name of the Transferor and/or the transferee(s) specified in such
Transferor Endorsement Form (each a "Transferee"), calling in the aggregate on
the face or faces thereof for the number of shares of Common Stock called for on
the face or faces of the Warrant so surrendered by the Transferor.

     10.  REPLACEMENT OF WARRANT. On receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Warrant
and, in the case of any such loss, theft or destruction of this Warrant, on
delivery of an indemnity agreement or security reasonably satisfactory in form
and amount to the Company or, in the case of any such mutilation, on surrender
and cancellation of this Warrant, the Company at its expense will execute and
deliver, in lieu thereof, a new Warrant of like tenor.

     11.  REGISTRATION RIGHTS. The Holder of this Warrant has been granted
certain registration rights by the Company. These registration rights are set
forth in a Registration Rights Agreement entered into by the Company and
Purchaser of the Company's Convertible Note (the "Note") at or prior to the
issue date of this Warrant.

     12.  MAXIMUM EXERCISE. The Holder shall not be entitled to exercise this
Warrant on an exercise date, in connection with that number of shares of Common
Stock which, when added to (i) the number of shares of Common Stock otherwise
beneficially owned by the Holder and its affiliates on an exercise date, and
(ii) the number of shares of Common Stock issuable upon the exercise of this
Warrant with respect to which the determination of this proviso is being made on
an exercise date, would result in beneficial ownership by the Holder and its
affiliates of more than 4.99% of the outstanding shares of Common Stock of the
Company on such date. For the purposes of the proviso to the immediately
preceding sentence, beneficial ownership shall be determined in accordance with
Section 13(d) of the Securities Exchange Act of 1934, as amended, and Regulation
13d-3 thereunder. Subject to the foregoing, the Holder shall not be limited to
aggregate exercises which would result in the issuance of more than 4.99%. The
restriction described in this paragraph may be revoked upon 75 days prior notice
from the Holder to the Company and is automatically null and void upon an Event
of Default under the Note.

     13.  WARRANT AGENT. The Company may, by written notice to the each holder
of the Warrant, appoint an agent for the purpose of issuing Common Stock (or
Other Securities) on the exercise of this Warrant pursuant to Section 1,
exchanging this Warrant pursuant to Section 7, and replacing this Warrant
pursuant to Section 8, or any of the foregoing, and thereafter any such
issuance, exchange or replacement, as the case may be, shall be made at such
office by such agent.

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     14.  TRANSFER ON THE COMPANY'S BOOKS. Until this Warrant is transferred on
the books of the Company, the Company may treat the registered holder hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary.

     15.  NOTICES, ETC. All notices and other communications from the Company to
the Holder of this Warrant shall be mailed by first class registered or
certified mail, postage prepaid, at such address as may have been furnished to
the Company in writing by such holder or, until any such Holder furnishes to the
Company an address, then to, and at the address of, the last Holder of this
Warrant who has so furnished an address to the Company.

     16.  VOLUNTARY ADJUSTMENT BY THE COMPANY. The Company may at any time
during the term of this Warrant reduce the then current Exercise Price to any
amount and for any period of time deemed appropriate by the Board of Directors
of the Company.

     17.  MISCELLANEOUS. This Warrant and any term hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought. This Warrant shall be governed by and construed in accordance with
the laws of State of New York without regard to principles of conflicts of laws.
Any action brought concerning the transactions contemplated by this Warrant
shall be brought only in the state courts of New York or in the federal courts
located in the state of New York; provided, however, that the Holder may choose
to waive this provision and bring an action outside the state of New York. The
individuals executing this Warrant on behalf of the Company agree to submit to
the jurisdiction of such courts and waive trial by jury. The prevailing party
shall be entitled to recover from the other party its reasonable attorney's fees
and costs. In the event that any provision of this Warrant is invalid or
unenforceable under any applicable statute or rule of law, then such provision
shall be deemed inoperative to the extent that it may conflict therewith and
shall be deemed modified to conform with such statute or rule of law. Any such
provision which may prove invalid or unenforceable under any law shall not
affect the validity or enforceability of any other provision of this Warrant.
The headings in this Warrant are for purposes of reference only, and shall not
limit or otherwise affect any of the terms hereof. The invalidity or
unenforceability of any provision hereof shall in no way affect the validity or
enforceability of any other provision. The Company acknowledges that legal
counsel participated in the preparation of this Warrant and, therefore,
stipulates that the rule of construction that ambiguities are to be resolved
against the drafting party shall not be applied in the interpretation of this
Warrant to favor any party against the other party.

          IN WITNESS WHEREOF, the Company has executed this Warrant under seal
as of the date first written above.

                                        TRANSGENOMIC, INC.


                                        By:  /s/ Michael J. Draper
                                           -------------------------------------
                                           Name: Michael J. Draper
                                           Title: CFO

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Witness:

     /s/ Keith A. Johnson
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