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                                                                   Exhibit 10.12

THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES
ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, ASSIGNED OR TRANSFERRED WITHOUT AN
EFFECTIVE REGISTRATION STATEMENT FOR SUCH SECURITIES UNDER THE SECURITIES ACT OF
1933, AS AMENDED, UNLESS THE COMPANY HAS RECEIVED THE WRITTEN OPINION OF COUNSEL
SATISFACTORY TO THE COMPANY TO THE EFFECT THAT SUCH SALE, ASSIGNMENT OR TRANSFER
DOES NOT INVOLVE A TRANSACTION REQUIRING REGISTRATION OF SUCH SECURITIES UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR APPLICABLE STATE SECURITIES LAWS.

                             CONVERTIBLE DEMAND NOTE

                                  May 10, 2004

         For value received, GIGABEAM CORPORATION, a Delaware corporation (the
"Company"), hereby unconditionally promises to pay to the order of AMERISTOCK
CORP. or its registered assigns (the "Payee"), ON DEMAND, the principal sum of
Two Hundred Thousand Dollars ($200,000.00), together with interest thereon, and
premium, if any, all as hereinafter provided, if not earlier converted pursuant
to the Agreement (as hereinafter defined). Such principal sum, together with all
interest incurred thereon, premium (if any), and all other fees and costs, shall
be due and payable ON DEMAND and, except as provided herein, the Payee's right
to make demand is unconditional and unlimited; notwithstanding the foregoing,
prior to the one year anniversary of the date of issuance of this Note (the
"Maturity Date"), the Payee may only make demand (if not earlier converted as
provided in the Agreement): (i) following the occurrence and continuance of an
Event of Default (as such term is defined in the Agreement) or (ii) immediately
prior to the closing of a Change of Control (as such term is defined in the
Agreement), which shall permit the acceleration and demand of this Note.

         The Company agrees that the Payee, in the exercise of the Payee's sole
discretion, may make demand at any time after the Maturity Date whether or not
any Event of Default or Change of Control has occurred and is continuing, and
may make demand at any time either before or after the Maturity Date in the
event of either of the occurrences described in items (i) and (ii) of the
immediately preceding paragraph of this Note. The Company agrees that, in
exercising its discretion, the Payee may make demand for any reasons which it
deems appropriate, and such reasons may be related or unrelated to the Company,
its business or financial condition or prospects. The Payee's right to make
demand is a continuing right, and acceptance by the Payee of any payment after
demand shall not be deemed a waiver of such right to make demand on any other
occasion.

         Prior to the date upon which the balance of this Note becomes due and
payable as described herein, whether by demand or otherwise (the "Payment Due
Date") and after the Payment Due Date, the unpaid principal balance outstanding
on all advances, from time to time, hereunder shall accrue interest at a rate
equal to ten percent (10%) per annum. Interest shall be compounded annually and
shall be computed on the basis of a 360-day year and a 30-day month.
Notwithstanding any other provision of this Note, the Payee does not intend to
charge and the Company shall not be required to pay any interest or other fees
or charges in excess of the maximum permitted by applicable law; any payments in
excess of such maximum shall be refunded to the Company or credited to reduce
principal hereunder. All payments received by the Payee hereunder will be
applied first to costs of collection and fees, if any, then to interest, then to
principal and the balance to premium (if any).

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         All principal plus accrued and unpaid interest on the Note and premium
(if any) shall be immediately due and payable upon notice in writing from Payee
to the Company, without presentment, demand, protest, or notice, upon the
occurrence of an Event of Default of the type specified in Section 4.1 of the
Agreement, after taking account of all applicable grace and cure periods
thereunder. All accrued and unpaid interest on the Note and premium (if any)
shall be paid upon payment of the principal of the Note, whether by demand, or
upon acceleration as provided herein, or otherwise. At the time that the payment
of the balance of this Note becomes due, the Payee may proceed with every remedy
available at law or in equity.

         This Note is issued pursuant to and is entitled to the benefits of a
certain Note and Warrant Purchase Agreement, dated as of April 19, 2004, by and
among the Company and the purchaser named therein (the "Agreement"), the terms
of which are incorporated herein, and each holder of this Note, by his, her or
its acceptance hereof, agrees to be bound by the provisions of the Agreement,
including, without limitation, the representations contained in Section 1.9
thereof. Without limiting the foregoing, the holder of this Note is subject to
the mandatory equity conversion provisions as set forth in Section 1.10 of the
Agreement.

         Principal and interest shall be payable in lawful money of the United
States of America, at the address of the Payee set forth in the Agreement or at
such other address as the Payee or any subsequent holder may designate from time
to time to the Company in writing. If any day on which a payment is due pursuant
to the terms of this Note is not a Business Day (as such term is defined in the
Agreement), such payment shall be due on the next Business Day following.

         Upon surrender of this Note for transfer or exchange, a new note or new
notes of the same tenor dated the date to which interest has been paid on the
surrendered Note and in an aggregate principal amount equal to the unpaid
principal amount of the Note so surrendered will be issued to, and registered in
the name of, the transferor or transferees. The Company may treat the person in
whose name this Note is registered as the owner hereof for the purpose of
receiving payment and for all other purposes.

         In the event any one or more of the provisions of this Note shall for
any reason be held to be invalid, illegal or unenforceable, in whole or in part
or in any respect, or in the event that any one or more of the provisions of
this Note operate or would prospectively operate to invalidate this Note, then
and in any such event, such provision(s) only shall be deemed null and void and
shall not affect any other provision of this Note and the remaining provisions
of this Note shall remain operative and in full force and effect and in no way
shall be affected, prejudiced, or disturbed thereby.

         In case any payment herein provided for shall not be paid when due, the
Company promises to pay all costs of collection or enforcement of this Note,
including, without limitation, court costs and all reasonable attorney's fees
and expenses incurred or paid by the Payee in enforcing the obligations of the
Company.



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         This Note may be not be prepaid without the prior written consent of
the Payee.

         All notices to the Company and the Payee required or permitted
hereunder shall be made in accordance with the Agreement.

         This Note shall be governed by, and construed in accordance with, the
laws of the State of Delaware.

         Whenever used herein, the terms "Company" and "Payee" shall be deemed
to include, to the extent applicable, the successors and assigns of such
parties; provided, however, that the obligations of the Company under this Note
may not be assigned without the express written consent of the Payee or any
holder hereof, which consent may be withheld in the sole and absolute discretion
of such Payee or holder.

         The Company and all endorsers of this Note herein waive presentment,
notice of nonpayment, protest and all other demand and notices in connection
with the delivery, acceptance, performance or enforcement of this Note.

         If any part of this Note shall be adjudged invalid, illegal, or
unenforceable, then such partial invalidity, illegality, or unenforceability
shall not cause the remainder of this Note to be or to become invalid, illegal,
or unenforceable. If a provision hereof is held invalid, illegal or
unenforceable in one or more of its applications, the parties hereto agree that
the other provisions shall remain in effect in all valid, legal and enforceable
applications that are severable from the invalid, illegal or unenforceable
application or applications.

         The validity, meaning, enforceability and effect of this Note, and the
rights and liabilities of the parties, shall be determined in accordance with
the laws of the State of Delaware.







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         IN WITNESS WHEREOF, the Company has executed this Note as of the date
and year first written above.

                                          GIGABEAM CORPORATION


                                          By:/s/ Louis Slaughter
                                             -----------------------------
                                          Name:    Louis Slaughter
                                          Title:   Chief Executive Officer


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