<PAGE>

                                                                     EXHIBIT 4.4

THIS WARRANT AND ANY SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE THEREOF HAVE
NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR UNDER ANY
STATE SECURITIES LAWS AND ACCORDINGLY MAY NOT BE SOLD, PLEDGED, TRANSFERRED,
ASSIGNED OR OTHERWISE DISPOSED OF EXCEPT IN ACCORDANCE WITH SUCH ACT AND THE
RULES AND REGULATIONS THEREUNDER AND IN ACCORDANCE WITH APPLICABLE STATE
SECURITIES LAWS. ZIX CORPORATION (THE "COMPANY") WILL TRANSFER SUCH WARRANT AND
ANY SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE THEREOF ONLY UPON RECEIPT OF
AN OPINION OF COUNSEL, IN FORM AND SUBSTANCE REASONABLY SATISFACTORY TO THE
COMPANY, THAT THE REGISTRATION PROVISIONS OF SUCH ACT HAVE BEEN COMPLIED WITH OR
THAT SUCH REGISTRATION IS NOT REQUIRED AND THAT SUCH TRANSFER WILL NOT VIOLATE
ANY APPLICABLE STATE SECURITIES LAWS.

                        COMMON STOCK WARRANT CERTIFICATE

                                 ZIX CORPORATION

January 30, 2004

                                           For the Purchase of 145,853 Shares of
                                           Common  Stock of Zix Corporation

         FOR VALUE RECEIVED, Aventis Holdings Inc., a Delaware corporation, or
its permitted assigns (the "Holder") is hereby granted the right to purchase
from Zix Corporation, a Texas corporation (the "Company"), up to a total of
145,853 shares (the "Warrant Shares", which number shall be adjusted from time
to time in accordance with Section 2 hereof) of the Company's common stock, par
value $.01 per share (the "Common Stock"), at a purchase price of $13.01 per
share (as adjusted from time to time in accordance with Section 2 hereof, the
"Exercise Price"), exercisable in whole or in part at any time and from time to
time from January 30, 2004 until 6:00 p.m. New York time on the date that is
three (3) years after the date hereof (the "Exercise Period"), on the terms and
conditions set forth in this Warrant (this "Warrant").

I.       EXERCISE.

         1.1      EXERCISE OF WARRANT. This Warrant may be exercised, in whole
or in part, at any time or from time to time, during the Exercise Period by (i)
surrendering this Warrant Certificate, with the form of exercise notice attached
hereto as Exhibit A duly executed by the Holder, to the Company at its principal
office, and (ii) (a) making payment to the Company of the aggregate Exercise
Price for the applicable Warrant Shares in cash, by certified check, bank check
or wire transfer to an account designated by the Company, or (b) providing
notice to the Company of the Holder's election to utilize the cashless exercise
feature of this Warrant set forth in Section 1.2 below; provided that the Holder
may only exercise this Warrant pursuant to clause (b) above if (1) the Common
Stock ceases to be listed on any of the Nasdaq National Market, the New York
Stock Exchange or the American Stock Exchange for a period of ten (10)
consecutive trading days, (2) the

<PAGE>

Company fails to obtain effectiveness of the Registration Statement (as defined
in the Registration Rights Agreement) in accordance with the Registration Rights
Agreement (as defined in Section 6.1) or (3) the Company fails to keep the
Registration Statement effective in accordance with the Registration Rights
Agreement. The minimum number of shares of Common Stock with respect to which
this Warrant may be exercised, in whole or in part, at any time shall be the
lesser of (1) ten percent (10%) of the total number of Warrant Shares which may
be purchased under this Warrant or (2) the maximum number of Warrant Shares
available for purchase under this Warrant at the time of exercise. Upon any
partial exercise of this Warrant, the Company, at its expense, shall promptly
issue to the Holder for Holder's surrendered Warrant Certificate a replacement
Warrant Certificate identical in all respects to this Warrant Certificate,
except that the number of Warrant Shares shall be reduced accordingly.

         1.2      CASHLESS EXERCISE. If the conditions to cashless exercise as
provided in Section 1.1(ii)(b) hereof are met, then the Holder may, in its sole
discretion, notify the Company in an exercise notice of its election to utilize
cashless exercise in accordance with the terms and conditions of Section 1.1
hereof, in which event the Company shall issue to the Holder the number of
Warrant Shares determined as follows:

               X = Y [(A-B) / A]

where:

               X =      the number of Warrant Shares to be issued to the Holder.

               Y =      the number of Warrant Shares with respect to which this
                        Warrant is being exercised.

               A =      the lower of (i) the average of the closing
                        prices for the twenty (20) trading days immediately
                        prior to, but not including, the Exercise Date (as
                        defined in Section 1.3) and (ii) the average of the
                        closing prices for the five (5) trading days
                        immediately prior to, but not including, the
                        Exercise Date (as defined in Section 1.3).

               B =      the Exercise Price.

For purposes of Rule 144 promulgated under the Securities Act (as defined in
Section 5.1), it is intended, understood and acknowledged that the Warrant
Shares issued in a cashless exercise transaction shall be deemed to have been
acquired by the Holder, and the holding period for the Warrant Shares shall be
deemed to have commenced, on the date this Warrant was originally issued.

         1.3      ISSUANCE OF WARRANT SHARES. The Warrant Shares purchased by
Holder shall be issued as of the close of business on the date on which all
actions required to be taken by the Holder and all payments required to be
received by the Company pursuant to Section 1.1, if the Holder is not using
cashless exercise pursuant to Section 1.2, shall have been so taken and
received, and the Holder shall be deemed for all corporate purposes to have
become the holder of record of such Warrant Shares as of such date (the
"Exercise Date"). Certificates for the Warrant Shares so

                                       2
<PAGE>

purchased shall be delivered to the Holder as soon as practicable (but in no
event more than five (5) days) after the Exercise Date.

II.      ADJUSTMENTS TO WARRANT.

         The number of Warrant Shares for which this Warrant is exercisable and
the Exercise Price shall be subject to adjustment from time to time as set forth
below.

         2.1      STOCK DIVIDENDS, SUBDIVISIONS AND COMBINATIONS. If the Company
shall, at any time or from time to time: (a) make (or fix a record date for the
holders of shares of its Common Stock entitled to receive) a dividend payable
in, or other distribution of, additional shares of Common Stock, (b) subdivide
its outstanding shares of Common Stock into a larger number of shares of Common
Stock, or (c) combine its outstanding shares of Common Stock into a smaller
number of shares of Common Stock, then (i) the number of Warrant Shares issuable
upon the exercise of this Warrant immediately prior to the occurrence of any
such event shall be adjusted so that the Holder of this Warrant upon exercise on
or after that date shall be entitled to receive the aggregate number of Warrant
Shares which the Holder of this Warrant would have owned and been entitled to
receive as a result of such event had this Warrant been exercised immediately
prior thereto, and (ii) the Exercise Price in effect immediately prior to such
event shall be adjusted by multiplying such Exercise Price by a fraction, the
numerator of which is the aggregate number of Warrant Shares purchasable upon
exercise of this Warrant immediately prior to such event, and the denominator of
which is the aggregate number of Warrant Shares purchasable upon exercise of
this Warrant immediately thereafter.

         2.2      DIVIDENDS AND DISTRIBUTIONS IN OTHER SECURITIES. If the
Company shall, at any time or from time to time, make (or fix a record date for
the holders of shares of its Common Stock entitled to receive) a dividend or
other distribution payable in other securities of the Company or in the
securities of any subsidiary of the Company (other than shares of Common Stock),
then lawful and adequate provision shall be made so that the Holder of this
Warrant shall be entitled to receive upon exercise of this Warrant, for the
aggregate Exercise Price in effect prior thereto, in addition to the number of
Warrant Shares immediately theretofore issuable upon exercise of this Warrant,
the kind and number of other securities of the Company or securities of any
subsidiary of the Company, which the Holder would have owned and been entitled
to receive had this Warrant been exercised immediately prior to that date.

         2.3      CASH DIVIDENDS AND DISTRIBUTIONS. If the Company shall, at any
time or from time to time, make (or fix a record date for the holders of shares
of its Common Stock entitled to receive) a dividend payable in, or other
distribution of cash, then the number of Warrant Shares issuable upon the
exercise of the Warrant, for the aggregate Exercise Price in effect prior
thereto, immediately prior to the occurrence of any such event shall be
increased by: (i) the amount of the dividend the Holder of this Warrant would
have received had the Holder exercised its warrant immediately prior to the
record date (or, if no record date has been set the date of distribution or
dividend), divided by (ii) the Current Market Price of the Company's Common
Stock. As used in this Warrant the term "Current Market Price" means with
respect to any security: (a) for so long as the issuer is a Public Entity (as
hereafter defined), and the security is traded on an organized exchange the
average closing price of the security on the stock exchange where the security
is traded or the last bid price as quoted on the NASDAQ for the immediately
preceding five (5) trading days; and (b) for so long as the issuer is not a
Public Entity or the security is not traded on

                                       3
<PAGE>

an organized exchange, the price per share of the security as determined in good
faith by the Company's board of directors. If such valuation is objected to by
the Holder of this Warrant, such valuation will be made by a reputable
investment bank of national standing mutually selected by the Holder and the
Company, the expense of which will be paid by the Company. "Public Entity" will
mean: (i) an entity that has registered its Common Stock pursuant to Section
12(b) or Section 12(g) of the Securities Exchange Act of 1934, as amended, and
(ii) the aggregate market value of Common Stock which is then available for
public trading is not less than Ten Million Dollars ($10,000,000), computed by
reference to the closing price of the Common Stock on the stock exchange where
the Common Stock is traded or the last bid price as quoted on the NASDAQ.

         2.4      REORGANIZATIONS, MERGERS, CONSOLIDATIONS OR SALES OF ASSETS.
If any of the following transactions (each, a "Special Transaction") shall
become effective: (a) a capital reorganization, whether by reclassification,
exchange, substitution or otherwise (other than a stock or cash dividend,
subdivision, combination or other distribution provided for elsewhere in this
Section 2), (b) a consolidation or merger of the Company with another entity, or
(c) a sale or conveyance of all or substantially all of the Company's assets;
then as a condition of any such Special Transaction, lawful and adequate
provision shall be made so that the Holder of this Warrant shall thereafter have
the right to purchase and receive upon exercise of this Warrant, in lieu of the
Warrant Shares immediately theretofore issuable upon exercise of this Warrant,
for the aggregate Exercise Price in effect immediately prior to such
consummation, such shares of stock, other securities, cash or other assets as
may be issued or payable in and pursuant to the terms of such Special
Transaction to the holders of shares of Common Stock for which this Warrant
could have been exercised immediately prior to such Special Transaction. In
connection with any Special Transaction, appropriate provision shall be made
with respect to the rights and interests of the Holder of this Warrant to the
end that the provisions of this Warrant (including without limitation the
provisions of this Section 2), shall thereafter be applicable, as nearly as may
be practicable, to any shares of stock, other securities, cash or other assets
thereafter deliverable upon the exercise of this Warrant.

         2.5      NOTICE. In the event that:

                  (a)      the Company shall fix a record date for the holders
         of shares of its Common Stock for the purpose of entitling them to
         receive any dividend or other distribution of shares of Common Stock or
         other securities of the Company; or

                  (b)      the Company shall enter into any agreement or adopt
         any plan for a Special Transaction; or

                  (c)      the Company shall adopt any plan for or otherwise
         shall become subject to any voluntary or involuntary dissolution,
         liquidation or winding up of the Company; or

                  (d)      the Company shall propose to take any other action
         which would require an adjustment pursuant to Sections 2.1 through 2.4,

then, and in each such case, the Company shall mail or cause to be mailed to the
Holder of this Warrant a notice specifying, as the case may be: (i) the date on
which a record is to be fixed for the purpose of such dividend or distribution,
and stating the amount and character of such dividend or distribution, or (ii)
the date on which such reorganization, consolidation, merger, conveyance,

                                       4
<PAGE>

dissolution, liquidation or winding up or other action is to become effective,
and the time, if any, to be fixed, as to which the holders of record of Common
Stock shall be entitled to exchange their shares of Common Stock for securities
or other property deliverable upon such reorganization, consolidation, merger,
conveyance, dissolution, liquidation or winding up or other action. Such notice
shall be mailed at least twenty (20) days prior to the date therein specified
and this Warrant may be exercised prior to said date during the Exercise Period.

         2.6      FRACTIONAL INTERESTS. The Company shall not be required to
issue fractions of shares of Common Stock upon the exercise of this Warrant. If
any fraction of a share of Common Stock would be issuable upon the exercise of
this Warrant, the Company shall, in lieu of such issuance, purchase such
fraction for an amount in cash equal to the current value of such fraction,
computed on the basis of the Current Market Price of the Common Stock on the
last business day prior to the date of exercise upon which such a sale of Common
Stock shall have been effected.

         2.7      EFFECT OF ALTERNATE SECURITIES. If at any time, as a result of
an adjustment made pursuant to this Section 2, the Holder of this Warrant shall
thereafter become entitled to receive any securities of the Company other than
shares of Common Stock, then the number of such other securities receivable upon
exercise of this Warrant shall be subject to adjustment from time to time on
terms as nearly equivalent as practicable to the provisions with respect to the
Warrant Shares as contained in this Section 2.

         2.8      SUCCESSIVE APPLICATION; READJUSTMENT. The provisions of this
Section 2 shall similarly apply from time to time to successive events covered
by this Section. If the Company shall fix a record date for the holders of its
Common Stock for the purpose of entitling them to receive a dividend or
distribution and shall, thereafter and before the distribution to shareholders
thereof, legally abandon its plan to pay or deliver such dividend or
distribution, then thereafter no adjustment shall be required by reason of the
taking of such record date and any such adjustment previously made in respect
thereof shall be rescinded and annulled.

         2.9      CERTIFICATE AS TO ADJUSTMENTS. In the event of an adjustment
in the number of Warrant Shares or in the Exercise Price, the Company at its
expense will promptly compute such adjustment in accordance with the terms of
this Warrant and prepare a certificate executed by an executive officer of the
Company setting forth such adjustment and showing in detail the facts upon which
such adjustment is based. The Company will forthwith mail a copy of each such
certificate to the Holder.

III.     RIGHTS OF THE HOLDER.

         3.1      NO RIGHTS AS SHAREHOLDER. The Holder shall not, solely by
virtue of this Warrant and prior to the issuance of the Warrant Shares upon due
exercise hereof, be entitled to any rights of a shareholder in the Company.

         3.2      NO IMPAIRMENT; CERTAIN COVENANTS. The Company shall not by any
action including, without limitation, amending its certificate of incorporation
or through any reorganization, transfer of assets, consolidation, merger,
dissolution, issue or sale of securities or any other voluntary action, avoid or
seek to avoid the observance or performance of any of the terms of this Warrant,
but will at all times in good faith assist in the carrying out of all such terms
and in the taking of all such actions as may be necessary or appropriate to
protect the rights of the

                                       5
<PAGE>

Holder against impairment. Without limiting the generality of the foregoing, the
Company will (a) take all such action as may be necessary or appropriate in
order that the Warrant Shares will, upon issuance in accordance with the terms
hereof and the payment of the Exercise Price therefor, be duly authorized,
validly issued and outstanding, fully paid and non-assessable, and free from all
taxes, liens and charges with respect to the issuance thereof, (b) at all times
during the Exercise Period have authorized and reserved sufficient shares of
Common Stock to provide for the exercise of this Warrant in full, and (c) use
its best efforts to obtain all such authorizations, exemptions or consents from
any public regulatory body having jurisdiction thereof as may be necessary to
enable the Company to perform its obligations under this Warrant.

         3.3      REGISTER. The Company shall maintain at its principal
executive offices (or such other office or agency of the Company as it may
designate by notice to Holder), a register for this Warrant in which the Company
shall record the name and address of the person in whose name this Warrant has
been issued, as well as the name and address of each assignee and/or transferee.
The Company may treat the person in whose name this Warrant is registered on the
register as the owner and holder thereof for all purposes, notwithstanding any
notice to the contrary, but in all events recognizing any transfers made in
accordance with the terms of this Warrant.

IV.      REPRESENTATIONS AND WARRANTIES OF THE COMPANY.

         The Company represents and warrants to and agrees with the Holder as
follows:

         4.1      SUFFICIENT SHARES. The Company has authorized sufficient
shares of Common Stock to fulfill the Company's obligations under this Warrant
and all of the other warrants, options and convertible securities issued by the
Company. On exercise of this Warrant and satisfaction of the Exercise Price, the
Warrant Shares issued to the Holder will be validly issued, fully paid,
non-assessable and free and clear of all liens, claims and encumbrances, except
any liens, claims, or encumbrances permitted by or imposed by the Holder.

         4.2      AUTHORITY. The Company has taken all necessary action to
authorize the execution and delivery of this Warrant and the issuance of the
Warrant Shares on the exercise of this Warrant. This Warrant is a valid, binding
and enforceable obligation of the Company. The execution, delivery and
performance of this Warrant will not violate: (a) any provision of the
organizational documents or charter of the Company; (b) any order, writ,
injunction or decree of any court, administrative agency or governmental body
applicable to the Company or the Common Stock; or (c) any contract, lease, note,
bond, mortgage or other agreement to which the Company is a party, by which the
Company is bound or to which any of the Company's assets are subject.

V.       RESTRICTIVE LEGEND.

         5.1      This Warrant is being acquired and any Warrant Shares to be
acquired by the Holder pursuant to this Warrant (collectively, "Securities")
will be acquired for investment for the Holder's own account and not for resale
in connection with any distribution of such Securities within the meaning of the
Securities Act of 1933, as amended (the "Securities Act"). The Securities will
not be sold, transferred or otherwise disposed of without registration under the
Securities Act and state securities laws or qualification for exemptions
therefrom. The Holder agrees that, until the Company has caused the registration
of such shares under the Securities Act, each certificate

                                       6
<PAGE>

evidencing the Warrant Shares may be inscribed with a legend to the foregoing
effect, which legend will be as follows:

                  The shares represented by this certificate have been acquired
                  solely for investment purposes and have not been registered
                  under the Securities Act of 1933, as amended, or the
                  securities laws of any state. The shares may not be sold,
                  transferred, assigned or otherwise disposed of unless and
                  until such shares are first registered under the Securities
                  Act of 1933, as amended, all applicable state securities laws
                  and all rules and regulations promulgated thereunder or unless
                  and until the holder hereof provides either (i) information
                  reasonably satisfactory to the Company that such registration
                  is not required or (ii) an opinion of counsel reasonably
                  acceptable to the Company to the effect that such registration
                  is not required.

VI.      REGISTRATION RIGHTS AGREEMENT.

         6.1      This Warrant and the Warrant Shares will qualify for all
benefits and be subject to the terms and conditions of that certain Registration
Rights Agreement of even date herewith among the Company, the Holder and Aventis
Inc. (the "Registration Rights Agreement"). The Holder agrees that each
certificate evidencing the Warrant Shares may be inscribed with a legend to the
foregoing effect as provided in the Registration Rights Agreement.

VII.     TRANSFER OR LOSS OF WARRANT.

         7.1      TRANSFER. Subject to compliance with federal and state
securities laws, the Holder may sell, assign, transfer or otherwise dispose of
all or any portion of this Warrant or the Warrant Shares acquired upon any
exercise hereof at any time and from time to time. Upon the sale, assignment,
transfer or other disposition of all or any portion of this Warrant, the Holder
shall deliver to Company a written notice of such in the form attached hereto as
Exhibit B duly executed by Holder which includes the identity and address of any
purchaser, assignor, or transferee. On such delivery, the Company will, subject
to conditions set forth herein, execute and deliver a new Warrant or Warrants in
the name of the assignee or assignees and in the denominations specified in such
instrument of assignment, and this Warrant will promptly be canceled. The
conditions to transferability specified in this Warrant are intended to provide
certain protections to the Holder and the Company and to ensure compliance with
the provisions of the Securities Act and applicable state securities laws in
respect of the transfer of any Warrant or any Warrant Shares and are to be
strictly construed.

         7.2      LOST, STOLEN, DESTROYED OR MUTILATED WARRANTS. In case any
Warrant is mutilated, lost, stolen or destroyed, the Company agrees to issue a
new Warrant of like date, tenor and denomination and deliver the same in
exchange and substitution for and upon surrender and cancellation of any
mutilated Warrant, or in lieu of any Warrant lost, stolen or destroyed, on
receipt of evidence reasonably satisfactory to the Company of the loss, theft or
destruction of such Warrant.

                                       7
<PAGE>

VIII.    MISCELLANEOUS.

         8.1      NOTICES. Any notice, demand or communication required or
permitted to be given by any provision of this Warrant must be in writing and
will be deemed to have been given and received when delivered personally or by
telefacsimile to the party designated to receive such notice, or on the date
following the day sent by overnight courier, or on the third (3rd) business day
after the same is sent by certified mail, postage and charges prepaid, directed
to the following addresses or to such other or additional addresses as any party
might designate by written notice to the other parties:

                  To the Company:                 Zix Corporation
                                                  2711 North Haskell Avenue
                                                  Suite 2850, LB 36
                                                  Dallas, Texas 75204-2911
                                                  Attn: Legal Department
                                                  Fax: (214) 370-2000

                  To the Holder:                  Aventis Holdings Inc.
                                                  3711 Kennett Pike
                                                  Greenville, DE  19807
                                                  Attn: President
                                                  Facsimile:

                  With a copy to:                 Aventis Pharmaceuticals Inc.
                                                  300 Somerset Corporate Blvd.
                                                  P.O. Box 6890, SC3-830A
                                                  Bridgewater, NJ  08807
                                                  Attn: General Counsel
                                                  Fax: (908) 243-7219

         8.2      EXPENSES; TAXES. Any sales tax, stamp duty, deed transfer or
other tax (except only taxes based on the income of Holder) arising out of the
issuance and sale of this Warrant or the Warrant Shares issuable upon exercise
of this Warrant and consummation of the transactions contemplated by this
Warrant Certificate shall be paid by the Company.

         8.3      AMENDMENT; WAIVER. This Warrant Certificate may not be
modified, amended, supplemented, canceled or discharged, except by written
instrument executed by the Company and the Holder. No failure to exercise, and
no delay in exercising, any right, power or privilege under this Warrant
Certificate shall operate as a waiver, nor shall any single or partial exercise
of any right, power or privilege hereunder preclude the exercise of any other
right, power or privilege. No waiver of any breach of any provision shall be
deemed to be a waiver of any preceding or succeeding breach of the same or any
other provision, nor shall any waiver be implied from any course of dealing
between the Company and the Holder. No extension of time for performance of any
obligations or other acts hereunder or under any other agreement shall be deemed
to be an extension of the time for performance of any other obligations or any
other acts.

                                       8
<PAGE>

         8.4      HEADINGS. The headings contained in this Warrant Certificate
are for convenience of reference only and are not to be given any legal effect
and shall not affect the meaning or interpretation of this Warrant Certificate.

         8.5      GOVERNING LAW. This Warrant is being delivered and is intended
to be performed in the State of Texas and will be construed and enforced in
accordance with, and the rights of the parties will be governed by, the law of
such state, without regard to its conflict of laws principles.

         8.6      SEVERABILITY. Should any part of this Warrant for any reason
be declared invalid, such decision shall not affect the validity of any
remaining portion, which remaining portion shall remain in full force and effect
as if this Warrant had been executed with the invalid portion thereof
eliminated, and it is hereby declared the intention of the parties hereto that
they would have executed and accepted the remaining portion of this Warrant
without including therein any such part, parts or portion which may, for any
reason, be hereafter declared invalid.

                  [Remainder of page intentionally left blank]

                                       9
<PAGE>

         IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be duly executed and delivered as of the day and year first above written.

                                     ZIX CORPORATION,
                                     a Texas corporation

                                     By: /s/ Ronald A. Woessner
                                         ----------------------------
                                         Name: Ronald A. Woessner
                                         Title: Senior Vice President

                            SIGNATURE PAGE TO WARRANT

<PAGE>

                                    EXHIBIT A

                                 EXERCISE NOTICE

                 [To be executed only upon exercise of Warrant]

                  The undersigned registered owner of the attached Warrant
Certificate irrevocably exercises this Warrant for the purchase of the number of
shares of Common Stock of Zix Corporation (the "Company") as is set forth below,
and herewith makes payment therefor, all at the price and on the terms and
conditions specified in the attached Warrant Certificate and requests that
certificates for the shares of Common Stock hereby purchased (and any securities
or other property issuable upon such exercise) be issued in the name of and
delivered to the person specified below whose address is set forth below, and,
if such shares of Common Stock shall not include all of the shares of Common
Stock now and hereafter issuable as provided in the attached Warrant
Certificate, then the Company shall, at its own expense, promptly issue to the
undersigned a new Warrant Certificate of like tenor and date for the balance of
the shares of Common Stock issuable thereunder.

Date:  ____________________

Amount of Shares Purchased: ______________

Aggregate Purchase Price: $_____________  OR  ___  Cashless Exercise

Printed Name of Registered Holder: _____________________________________________

Signature of Registered Holder: ________________________________________________

NOTICE:  The signature on this Exercise Notice must correspond with the name as
         written upon the face of the attached Warrant Certificate in every
         particular, without alteration or enlargement or any change whatsoever.

Stock Certificates to be issued and registered in the following name, and
delivered to the following address:

                                             ___________________________________
                                             (Name)
                                             ___________________________________
                                             (Street Address)
                                             ___________________________________
                                             (City)         (State) (Zip Code)

<PAGE>

                                    EXHIBIT B

                                ASSIGNMENT NOTICE

                 [To be executed only upon transfer of Warrant]

         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto the person named below, whose address is set forth below, the rights
represented by the attached Warrant Certificate to purchase the number of shares
of Common Stock of Zix Corporation (the "Company") as is set forth below, to
which the attached Warrant Certificate relates, and appoints ___________
_________________ attorney to transfer such rights on the books of the Company
with full power of substitution in the premises. If such shares of Common Stock
of the Company shall not include all of the shares of Common Stock now and
hereafter issuable as provided in the attached Warrant Certificate, then the
Company, at its own expense, shall promptly issue to the undersigned a new
Warrant Certificate of like tenor and date for the balance of the Common Stock
issuable thereunder.

Date: ____________________

Amount of Shares Purchased: ______________

Aggregate Purchase Price: $_____________

Printed Name of Registered Holder: ____________________________________________

Signature of Registered Holder: _______________________________________________

         NOTICE:           The signature on this Assignment Notice must
                           correspond with the name as written upon the face of
                           the attached Warrant Certificate in every particular,
                           without alteration or enlargement or any change
                           whatsoever.

Warrant Certificate for transferred Warrants to be issued and registered in the
following name, and delivered to the following address:

                                          ____________________________________
                                          (Name)

                                          ____________________________________
                                          (Street Address)

                                          ____________________________________
                                          (City)            (State) (Zip Code)