<PAGE>   1





              ADVANCING PROMISSORY NOTE CONVERTING TO A TERM NOTE
                                 (this "Note")

<TABLE>
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  U.S. $4,700,000.00                                      July 21, 1997 (the "DATE")
  ACCOUNT  NUMBER:             NOTE NUMBER:               RENEWAL CODE:               TELLER:                 OFFICER:
  <S>                          <C>                        <C>                         <C>                     <C>
  --------------------------   -----------------------              -----             -------------------     ---------------
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</TABLE>

FOR VALUE RECEIVED, FRIEDMAN INDUSTRIES, INCORPORATED (the "Maker"), a Texas
corporation, promises to pay to the order of TEXAS COMMERCE BANK NATIONAL
ASSOCIATION (the "Bank") on or before August 1, 2003 (the "Stated Maturity
Date"), at its banking house at 712 Main Street, Houston, Harris County, Texas,
or at such other location as the Bank may designate, in lawful money of the
United States of America, the lesser of: (i) the principal sum of FOUR MILLION
SEVEN HUNDRED THOUSAND AND NO 100THS DOLLARS (U.S. $4,700,000.00) or (ii) the
aggregate unpaid principal amount of all loans made by the Bank hereunder (each
such loan being a "Loan"), which may be outstanding on the Stated Maturity Date
("Maximum Loan Total").  Each Loan shall be due and payable on the Interest
Period maturity date agreed to by the Bank and the Maker with respect to such
Loan (the "Maturity Date"), provided that the principal of any Loan that
becomes due and payable on a Maturity Date preceding the Stated Maturity Date
and that is not repaid on such Maturity Date (with the proceeds of a Loan made
by the Bank at the request of the Maker or otherwise) shall be deemed to be
automatically (without the requirement of any request for advance or other
action on the part of the Maker) repaid in full by an advance of (and such
maturing Loan shall automatically be deemed to be converted to) a LIBOR Loan
for an Interest Period of 30 days.

The Loans shall be LIBOR Loans (as hereinafter defined).

The Maker shall pay interest on each LIBOR Loan for the Interest Period with
respect thereto on the unpaid principal amount thereof at a rate per annum
equal to the lesser of: (i) the LIBOR Rate (as hereinafter defined) plus one
and one quarter of one percent (1.250%) (the "Effective LIBOR Rate"); or (ii)
the Highest Lawful Rate, which interest shall be due and payable on the last
day of each such Interest Period, and if such Interest Period has a duration
exceeding one month, on the first day of each month during such Interest
Period.

The unpaid principal balance of this Note at any time shall be the total
amounts loaned or advanced by the Bank or holder hereof, less the amount of all
payments or prepayments of principal made hereon by or for the Maker.  Absent
manifest error, the records of the Bank or any subsequent holder shall be
conclusive as to amounts owed, both principal and accrued interest, hereunder.
Subject to the terms and conditions of this Note and the Credit Agreement (as
defined below), and provided that no Event of Default has occurred, Maker may
use all or any part of the credit provided for herein at any time before
December 1, 1998 (the "Advance Termination Date") and may borrow and repay but
not reborrow hereunder prior to the Advance Termination Date.  There is no
limitation on the number of advances made hereunder so long as the total amount
advanced prior to the Advance Termination Date does not exceed the Maximum Loan
Total.

Advances against this Note by the Bank or other owner or holder hereof shall be
governed by the terms and conditions hereof, and that one certain Amended and
Restated Letter Agreement by and between Bank and maker dated as of April 1,
1995 as amended by a First Amendment dated as of April 1, 1997 and a Second
Amendment dated as of July 21, 1997, and including any amendments,
modifications, supplements thereto and restatements thereof (the "Credit
Agreement").

Principal payments of $200,000.00 each plus accrued interest shall be due and
payable quarterly, beginning on September 1, 1997, and continuing on the first
(1st) day of each June, September, December, and March thereafter and at the
Stated Maturity Date when all unpaid principal and accrued and unpaid interest
shall be finally due and payable.

Any amount not paid when due with respect to principal (whether at Maturity
Date, by acceleration or otherwise), costs, expenses, and to the extent
permitted by applicable law, interest, shall bear interest at a rate per annum
equal to the lesser of: (i) the Prime Rate (as herein defined) in effect from
time to time; or (ii) the Highest Lawful Rate, which interest shall be due and
payable on demand.  The principal of any Loan shall be deemed past due if not
paid on or before the Maturity Date or any earlier maturity date resulting from
acceleration in accordance with the terms of this Note or as provided by law or
otherwise.  Interest accrued and unpaid with respect to any Loan shall be
deemed past due if not paid on or before the applicable interest payment due
date as provided for herein.

Notwithstanding the foregoing, if at any time the effective rate of interest
which would otherwise be payable on any Loan evidenced by this Note exceeds the
Highest Lawful Rate, the rate of interest to accrue on the unpaid principal
balance of such Loan during all such times shall be limited to the Highest
Lawful Rate, but any subsequent reductions in such interest rate shall not
become effective to reduce such interest rate below the Highest Lawful Rate
until the total amount of interest accrued on the unpaid principal balance of
such Loan equals the total amount of interest which would have accrued if the
Effective LIBOR Rate, had at all times been in effect.

Each Loan shall be in an amount not less than $10,000.00 and an integral
multiple of $10,000.00.  Interest with respect to Prime Rate Loans shall be
calculated on the basis of a 365 day year or 366 day year, as the case may be,
for the actual number of days elapsed.  Interest with respect to LIBOR Loans
shall be calculated on the basis of a 360 day year for the actual days elapsed,
unless such calculation would result in a usurious interest rate, in which case
such interest shall be calculated on the basis of a 365 day or 366 day year, as
the case may be.

The following terms shall have the respective meanings indicated:

         "Board" shall mean the Board of Governors of the Federal Reserve
         System of the United States.

         "Borrowing Date" means any Business Day on which the Bank shall make a
         Loan hereunder.

                              Page 1 of 4 Pages

                                                       Signed for Identification
                                                           By: /s/ ILLEGIBLE
                                                               ---------------
<PAGE>   2

         "Business Day" means a day: (i) on which the Bank and commercial banks
         in New York City are generally open for business; and (ii) with
         respect to LIBOR Loans, on which dealings in United States Dollar
         deposits are carried out in the Eurodollar interbank markets.

         "Eurodollar Lending Office" means the office of the Bank located at
         712 Main Street, Houston, Texas, or such other office of the Bank as
         the Bank may from time to time specify to the Maker.

         "LIBOR Loan" means a Loan which bears interest at a rate determined by
         reference to the LIBOR Rate.

         "LIBOR Rate" means, for each LIBOR Loan, an interest rate per annum
         determined by the Bank by dividing: (i) for any Interest Period, the
         interest rate determined by Bank by reference to the British Bankers'
         Association Interest Settlement Rates (as set forth on Telerate Page
         3750 or any successor or substitute page; or if unavailable there, by
         any service selected by Bank which has been nominated by the British
         Bankers' Association as an authorized information vendor for the
         purpose of displaying such rates including but not limited to
         Bloomberg or Reuters) to be the rate at approximately 11:00 a.m.
         London time, two Business Days prior to the commencement of such
         Interest Period for dollar deposits in an amount comparable to such
         LIBOR Loan with a maturity comparable to such Interest Period; by (ii)
         Statutory Reserves.

         "Highest Lawful Rate" as used herein shall mean the maximum
         nonusurious interest rate permitted from time to time to be contracted
         for, taken, reserved, charged or received on any Loan under applicable
         federal or Texas laws, whichever permits the higher lawful rate;
         provided, however, that in the event: (i) such maximum nonusurious
         interest rate shall, at any time or times during the term of a Loan
         evidenced hereby, be reduced to a rate less than the maximum
         nonusurious rate in effect on the date of such Loan; and (ii)
         applicable law permits contracting for, taking, reserving, charging,
         and receiving on such Loan throughout the duration thereof the maximum
         nonusurious rate in effect on the date such Loan was made, then and at
         all such times the Highest Lawful Rate shall be the maximum
         nonusurious rate permitted to be contracted for, taken, reserved,
         charged or received on such Loan under applicable law in effect on the
         date of such Loan.  At all such times, if any, as Texas law shall
         establish the Highest Lawful Rate, the Highest Lawful Rate shall be
         the "indicated rate ceiling" (as defined in Tex. Rev. Civ. Stat. art.
         5069-1.04) from time to time in effect.

         "Interest Period" means the period commencing on the Borrowing Date
         and ending on the Maturity Date.  The duration of each Interest Period
         shall be 30 days.   No Interest Period shall end on a date after the
         Stated Maturity Date, and if the last day of an Interest Period would
         be a day other than a Business Day, the Interest Period shall end on
         the next succeeding Business Day (unless the Interest Period relates
         to a LIBOR Loan and the next succeeding Business Day is in a different
         calendar month than the day on which the Interest Period would
         otherwise end, in which case the Interest Period shall end on the next
         preceding Business Day).

         "Prime Rate" shall mean the rate of interest per annum determined from
         time to time by the Bank as its prime rate in effect at its principal
         office in Houston, Texas and thereafter entered in the minutes of its
         Loan and Discount Committee; each change in the Prime Rate shall be
         effective on the date such change is determined; without special
         notice to the Maker or any other person or entity.  THE PRIME RATE IS
         A REFERENCE RATE AND DOES NOT NECESSARILY REPRESENT THE LOWEST OR BEST
         RATE ACTUALLY CHARGED TO ANY CUSTOMER AND ANY STATEMENT,
         REPRESENTATION OR WARRANTY IN THAT REGARD OR TO THAT EFFECT IS
         EXPRESSLY DISCLAIMED BY THE BANK. THE BANK MAY MAKE LOANS AT RATES OF
         INTEREST AT, ABOVE OR BELOW THE PRIME RATE.

         "Statutory Reserves" shall mean the difference (expressed as a
         decimal) of the number one minus the aggregate of the maximum reserve
         percentages (including, without limitation, any marginal, special,
         emergency, or supplemental reserves) expressed as a decimal
         established by the Board and any other banking authority to which the
         Bank is subject: (a) with respect to the LIBOR Rate, for Eurocurrency
         Liabilities (as defined in Regulation D of the Board).  Such reserve
         percentages shall include, without limitation, those imposed under
         such Regulation D.  LIBOR Loans shall be deemed to constitute
         Eurocurrency Liabilities and as such shall be deemed to be subject to
         such reserve requirements without benefit of or credit for proration,
         exceptions or offsets which may be available from time to time to any
         Bank under such Regulation D.  Statutory Reserves shall be adjusted
         automatically on and as of the effective date of any change in any
         reserve percentage.

Any Loan which the Bank makes hereunder shall be made on the Maker's
irrevocable notice, given not later than 10:00 A.M.  (Houston, Texas time) on,
in the case of LIBOR Loans, the third Business Day prior to the proposed
Borrowing Date from the Maker to the Bank.  Each such notice of a requested
borrowing (a "Notice of Requested Borrowing") under this paragraph may be oral
or written, and shall specify: (i) the requested amount of such Loan; (ii) the
proposed Borrowing Date; (iii) that the requested Loan is to be a 30 day LIBOR
Loan.  If any Notice of Requested Borrowing shall be oral, the Maker shall
deliver to the Bank prior to the Borrowing Date a confirmatory written Notice
of Requested Borrowing.

If at any time the Bank determines in good faith (which determination shall be
conclusive) that any change in any applicable law, rule or regulation or in the
interpretation, application or administration thereof makes it unlawful, or any
central bank or other governmental authority asserts that it is unlawful, for
the Bank or its foreign branch or branches to maintain or fund any Loan by
means of dollar deposits obtained in any Eurodollar interbank market (any of
the above being described as a "Eurodollar Event"), then, at the option of the
Bank, the aggregate principal amount of the Bank's LIBOR Loans then
outstanding, which Loans are directly affected by such Eurodollar Event, shall
be prepaid by the Maker.  Upon the occurrence of any Eurodollar Event, and at
any time thereafter so long as such Eurodollar Event shall continue, the Bank
may exercise its aforesaid option by giving written notice thereof to the
Maker.

Any prepayment of any LIBOR Loan which is required under the preceding
paragraph shall be made, together with accrued and unpaid interest and all
other amounts payable to the Bank under this Note with respect to such prepaid
LIBOR Loan on the date stated in the notice to the Maker referred to above,
which date ("required prepayment date") shall be not less than 15 days from the
date of such notice.  If any LIBOR Loan is required to be prepaid under the
preceding paragraph, the Bank shall make on the required





                               Page 2 of 4 Pages
                                                      Signed for Identification 
                                                            By: /s/ ILLEGIBLE
                                                                ---------------
<PAGE>   3

prepayment date a Prime Rate Loan in the same principal amount and with an
Interest Period ending on the same day as the LIBOR Loan so prepaid.

If any domestic or foreign law, treaty, rule or regulation (whether now in
effect or hereinafter enacted or promulgated, including Regulation D of the
Board of Governors of the Federal Reserve System) or any interpretation or
administration thereof by any governmental authority charged with the
interpretation or administration thereof (whether or not having the force of
law):

         (a)     changes, imposes, modifies, applies or deems applicable any
                 reserve, special deposit or similar requirements in respect of
                 any such Loan or against assets of, deposits with or for the
                 account of, or credit extended or committed by, the Bank; or

         (b)     imposes on the Bank or the interbank eurocurrency deposit and
                 transfer market or the market for domestic bank certificates
                 or deposit any other condition affecting any such Loan;

and the result of any of the foregoing is to impose a cost to the Bank of
agreeing to make, funding or maintaining any such Loan or to reduce the amount
of any sum receivable by the Bank in respect of any such Loan, then the Bank
may notify the Maker in writing of the happening of such event and the Maker
shall upon demand pay to the Bank such additional amounts as will compensate
the Bank for such costs.  Without prejudice to the survival of any other
agreement of the Maker under this Note, the obligations of the Maker under this
paragraph shall survive the termination of this Note.

The Maker may from time to time, on the applicable Maturity Date of any LIBOR
Loan, pay or prepay the outstanding principal amount of such LIBOR Loan, in
whole or in part, together with accrued interest to the date of such prepayment
on the principal amount prepaid.

Notwithstanding the previous paragraph, the Maker may from time to time prepay
any Loan on any Business Day, provided that if the date for such prepayment is
not a Maturity Date then the Maker shall indemnify the Bank against, and
reimburse the Bank on demand for, any loss, cost or expense incurred or
sustained by the Bank (including without limitation any loss, cost or expense
incurred by reason of the liquidation or reemployment of deposits or other
funds acquired by the Bank to fund or maintain Loans bearing interest at the
LIBOR Rate) as a result of: (a) any payment or prepayment (whether permitted by
the Bank or required hereunder or otherwise) of all or a portion of any LIBOR
Loan on a day other than the Maturity Date of such Loan; (b) any payment or
prepayment, whether required hereunder or otherwise, of any LIBOR Loan made
after the delivery of a Notice of Requested Borrowing but before the applicable
Borrowing Date if such payment or prepayment prevents the proposed Loan from
becoming fully effective; or (c) the failure of any LIBOR Loan to be made by
the Bank due to any action or inaction of the Maker.  For purposes of this
paragraph, funding losses arising by reason of liquidation or reemployment of
deposits or other funds acquired by the Bank to fund or maintain Loans bearing
interest at the LIBOR Rate shall be calculated as the remainder obtained by
subtracting:  (i) the yield (reflecting both stated interest rate and discount,
if any) to maturity of obligations of the United States Treasury in an amount
equal or comparable to such Loan for the period of time commencing on the date
of the payment, prepayment or change of rate as provided above and ending on
the last day of the subject Interest Period; from (ii) the interest payable at
the LIBOR Rate for the period commencing on the date of such payment,
prepayment or change of rate and ending on the last day of such Interest
Period.  Such funding losses and other costs and expenses shall be calculated
and billed by the Bank and such bill shall, as to the costs incurred, be
conclusive absent manifest error.

If after the date of this Note, the Bank shall have determined that the
adoption of any applicable law, rule or regulation regarding capital adequacy,
or any change therein, or any change in the interpretation or administration
thereof by any governmental authority, central bank or comparable agency
charged with the interpretation or administration thereof, or compliance by the
Bank with any request or directive regarding capital adequacy (whether or not
having the force of law) of any such authority, central bank or comparable
agency, has or would have the effect of reducing the rate of return on the
Bank's capital as a consequence of making any Loans hereunder to a level below
that which the Bank could have achieved but for such adoption, change or
compliance (taking into consideration the Bank's policies with respect to
capital adequacy) by an amount deemed by the Bank in good faith to be material,
then from time to time, the Maker shall pay to the Bank such additional amount
or amounts as will compensate the Bank for such reduction.

A certificate of the Bank setting forth such amount or amounts as shall be
necessary to compensate the Bank as specified in the immediately four preceding
paragraphs above shall be delivered as soon as practicable to the Maker and
shall be conclusive and binding, absent manifest error, provided that such
certificate is prepared in good faith and on a reasonable basis.  The Maker
shall pay the Bank the amount shown as due on any such certificate within 15
days after the Bank delivers such certificate.  In preparing such certificate,
the Bank may employ such assumptions and allocations of costs and expenses as
it shall in good faith deem reasonable and may use any reasonable averaging and
attribution method.

If any payment of interest or principal herein provided for is not paid when
due then the owner or holder of this Note may at its option, by notice to the
Maker, declare the unpaid principal balance of all Loans, all accrued and
unpaid interest thereon and all other amounts payable under this Note to be
forthwith due and payable, whereupon the Loans, all such interest and all such
amounts shall become and be forthwith due and payable in full, without
presentment, demand, protest, notice of intent to accelerate, notice of actual
acceleration or further notice of any kind, all of which are hereby expressly
waived by the Maker.

If default is made in the payment of this Note and it is placed in the hands of
an attorney for collection, or collected through probate or bankruptcy
proceedings, or if suit is brought on the same, the Maker agrees to pay
reasonable attorneys' fees and all costs and expenses.

The Maker warrants and represents to the Bank, and to all other owners and/or
holders of any indebtedness evidenced hereby, that all Loans evidenced by this
Note are for business, commercial, investment or other similar purpose and not
primarily for personal, family, household or agricultural use, as such terms
are used in Chapter One of the Texas Credit Code, Tex. Rev. Civ. Stat. arts.
5069-1.01 et. seq.





                               Page 3 of 4 Pages
                                                      Signed for Identification 
                                                             By: /s/ ILLEGIBLE
                                                                ----------------
<PAGE>   4
The Maker warrants and represents to the Bank and to all other owners or
holders of this Note that no Loans shall be used for the purchase or carrying
of any "margin stock" within the meaning of Regulation "U" of the Board of
Governors of the Federal Reserve System, 12 C.F.R. Part 221, as in effect on
the date hereof.

Except as otherwise specified in this Note, the Maker and any and all
co-makers, endorsers, guarantors and sureties hereby severally waive grace,
presentment, demand, notice of default, notice of intent to accelerate, notice
of acceleration, and all other demands and notices of any nature or type
whatsoever, in connection with the delivery, acceptance, performance, default,
dishonor or enforcement of, or entry of judgment in connection with this Note,
and further waive the filing of suit hereon for the purpose of fixing
liability.

THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE
STATE OF TEXAS AND THE APPLICABLE LAWS OF THE UNITED STATES OF AMERICA.  THIS
NOTE SHALL BE PERFORMABLE FOR ALL PURPOSES IN HARRIS COUNTY, TEXAS, AND THE
MAKER AND THE BANK AGREE THAT HARRIS COUNTY, TEXAS IS PROPER VENUE FOR ANY
ACTION OR PROCEEDING BROUGHT BY THE MAKER OR THE BANK, WHETHER IN CONTRACT,
TORT, OR OTHERWISE.  ANY ACTION OR PROCEEDING AGAINST THE MAKER MAY BE BROUGHT
IN ANY STATE OR FEDERAL COURT IN HARRIS COUNTY, TEXAS.  THE MAKER HEREBY
IRREVOCABLY (A) SUBMITS TO THE NONEXCLUSIVE JURISDICTION OF SUCH COURTS, AND
(B) WAIVES ANY OBJECTION IT MAY NOW OR HEREAFTER HAVE AS TO THE VENUE OF ANY
SUCH ACTION OR PROCEEDING BROUGHT IN ANY SUCH COURT OR THAT ANY SUCH COURT IS
AN INCONVENIENT FORUM.  THE MAKER AGREES THAT SERVICE OF PROCESS UPON IT MAY BE
MADE BY CERTIFIED OR REGISTERED MAIL, RETURN RECEIPT REQUESTED, AT ITS ADDRESS
SPECIFIED BELOW.

The Maker and the Bank expressly agree, pursuant to Article 15.10(b) of Chapter
15 ("Chapter 15") of the Texas Credit Code, that Chapter 15 shall not apply to
this Note or to any Loan and that this Note and all such Loans shall not be
governed by or subject to the provisions of Chapter 15 in any manner
whatsoever.

It is the intention of the Maker and the Bank to comply with usury laws in
force in the State of Texas and in the United States of America as applicable.
Anything in this Note to the contrary notwithstanding, the Maker shall never be
required to pay unearned interest on this Note and shall never be required to
pay interest on this Note at a rate in excess of the Highest Lawful Rate, and
if the effective rate of interest which would otherwise be payable under this
Note would exceed the Highest Lawful Rate, or if the holder of the Note shall
receive any unearned interest or shall receive monies that are deemed to
constitute interest which would increase the effective rate of interest payable
under this Note to a rate in excess of the Highest Lawful Rate, then: (i) the
amount of interest which would otherwise be payable under this Note shall be
reduced to the amount allowed under applicable law; and (ii) any unearned
interest paid by the Maker or any interest paid by the Maker in excess of the
Highest Lawful Rate shall, at the option of the holder of this Note, be either
refunded to the Maker or credited on the principal of this Note.  It is further
agreed that, without limitation of the foregoing, all calculations of the rate
of interest contracted for, charged or received by the Bank or any holder of
this Note that are made for the purpose of determining whether such rate
exceeds the Highest Lawful Rate shall be made, to the extent permitted by usury
laws applicable to the Bank (now or hereafter enacted), by amortizing,
prorating and spreading in equal parts during the period of the full stated
term of the Loans evidenced by this Note all interest at any time contracted
for, charged or received by the Bank in connection therewith.

The Bank reserves the right in its sole discretion without notice to the Maker,
to sell participations or assign its interest, or both in all or part of the
Loans, the Note, or the Line of Credit.

         THIS NOTE AND THE OTHER LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT
BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES.

         THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

IN WITNESS WHEREOF, the Maker has executed this Note effective the day, month
and year first aforesaid.

MAKER:  FRIEDMAN INDUSTRIES, INCORPORATED

By: /s/ BEN HARPER
   _____________________________________________________________________________

Name: Ben Harper 
     ___________________________________________________________________________

Title: Senior Vice President-Finance
      __________________________________________________________________________

Acknowledged for purposes of notice pursuant to the above cited statute by:

TEXAS COMMERCE BANK NATIONAL ASSOCIATION

By:_____________________________________________________________________________

Name:___________________________________________________________________________

Title:__________________________________________________________________________





                               Page 4 of 4 Pages
                                                      Signed for Identification 
                                                                  By:_____