<PAGE>
 
                                                                    EXHIBIT 4(b)
                                                                                
UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), TO THE ISSUER OR ITS
AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE
ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS
REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO
CEDE & CO., OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

THIS SECURITY IS A BOOK-ENTRY SECURITY WITHIN THE MEANING OF THE INDENTURE
HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF A DEPOSITORY OR A
NOMINEE OF A DEPOSITORY.  THIS SECURITY IS EXCHANGEABLE FOR SECURITIES
REGISTERED IN THE NAME OF A PERSON OTHER THAN THE DEPOSITORY OR ITS NOMINEE ONLY
IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE AND MAY NOT BE
TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITORY TO A NOMINEE OF THE DEPOSITORY
OR BY A NOMINEE OF THE DEPOSITORY TO THE DEPOSITORY OR ANOTHER NOMINEE OF THE
DEPOSITORY.

                            ALBERTO-CULVER COMPANY

                      6.375% Debentures due June 15, 2028

Number 1                                                            $120,000,000

                                                             CUSIP No. 013068AC5

    ALBERTO-CULVER COMPANY, a corporation duly organized and existing under the
laws of the State of Delaware (herein called the "Company," which term includes
any successor corporation under the Indenture hereinafter referred to), for
value received, hereby promises to pay to CEDE & CO., or registered assigns, the
principal sum of One Hundred and Twenty Million Dollars ($120,000,000) on June
15, 2028 and to pay interest thereon from June 15, 1998 or from the most recent
Interest Payment Date to which interest has been paid or duly provided for, 
semi-annually on June 15 and December 15 in each year, commencing December 15,
1998, at the rate of 6.375% per annum, until the principal hereof is paid or
made available for payment. The interest so payable, and punctually paid or duly
provided for, on any Interest Payment Date will, as provided in such Indenture,
be paid to the Person in whose name this Security (or one or more Predecessor
Securities) is registered at the close of business on the Regular Record Date
for such interest, which shall be the June 1 or December 1 (whether or not a
Business Day), as the case may be, next preceding such Interest Payment Date.
Any such interest not so punctually paid or duly provided for will forthwith
cease to be payable to the Holder on such Regular Record Date and may either be
paid to the Person in whose name this

<PAGE>
 
Security (or one or more Predecessor Securities) is registered at the close of
business on a Special Record Date for the payment of such Defaulted Interest to
be fixed by the Trustee, notice whereof shall be given to Holders of Securities
of this series not less than 10 days prior to such Special Record Date, or be
paid at any time in any other lawful manner not inconsistent with the
requirements of any securities exchange on which the Securities of this series
may be listed, and upon such notice as may be required by such exchange, all as
more fully provided in said Indenture.

    Payment of the principal of (and premium, if any) and interest on this
Security will be made in such coin or currency of the United States of America
as at the time of payment is legal tender for payment of public and private
debts.  Payment of the principal of, and premium if any, on the Security will be
made at the office or agency of the Company maintained for that purpose in New
York, New York.  Payment of the interest on this Security will be paid to the
person entitled thereto by wire transfer in immediately available funds on each
applicable Interest Payment Date, not later than 2:30 P.M. Eastern Standard
Time.

    Reference is hereby made to the further provisions of this Security
set forth on the reverse hereof, which further provisions shall for all purposes
have the same effect as if set forth at this place.

    Unless the certificate of authentication hereon has been executed by
the Trustee referred to on the reverse hereof by manual signature, this Security
shall not be entitled to any benefit under the Indenture or be valid or
obligatory for any purpose.

    IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed under its corporate seal.


                                       ALBERTO-CULVER COMPANY

Dated: June 15, 1998
                                       By: /s/ William J. Cernugel
                                           -------------------------------------
                                               William J. Cernugel
                                               Senior Vice President, Finance
                                               and Controller
Attest:
/s/ Gary P. Schmidt
 ....................................
Assistant Secretary

    This is one of the Securities of the series designated therein referred to
in the within-mentioned Indenture.


                                       THE FIRST NATIONAL BANK OF CHICAGO
                                         As Trustee

                                       By: /s/ Brenda McCleod
                                           -------------------------------------
                                               Trust Officer
<PAGE>
 

          This Security is one of a duly authorized issue of securities of the
Company (herein called the "Securities"), issued and to be issued in one or more
series under an Indenture, dated as of June 10, 1998 (herein called the
"Indenture"), between the Company and The First National Bank of Chicago, as
Trustee (herein called the "Trustee," which term includes any successor trustee
under the Indenture), to which Indenture and all indentures supplemental thereto
reference is hereby made for a statement of the respective rights, limitations
of rights, duties and immunities thereunder of the Company, the Trustee and the
Holders of the Securities and of the terms upon which the Securities are, and
are to be, authenticated and delivered. This Security is one of the series
designated on the face hereof, limited, except as provided in the Indenture, in
aggregate principal amount to $120,000,000.

          The Securities of this series are subject to redemption upon not less
than 30 days and not more than 60 days notice by mail, at any time, in whole or
in part, at the option of the Company, at a redemption price equal to (a) prior
to and including June 15, 2008, the greater of (i) 100% of the principal amount
of such Debentures, (ii) the sum of the present values of the remaining
scheduled payments of principal (as if such principal was scheduled to be paid
on June 15, 2008 rather than June 15, 2028) and interest thereon (not including
the portion of any such payments of interest accrued as of the redemption date)
up to June 15, 2008 or (iii) the sum of the present values of the remaining
scheduled payments of principal and interest thereon (not including the portion
of any such payments of interest accrued as of the redemption date) up to June
15, 2028 or (b) from June 15, 2008 to June 15, 2028, the greater of (i) 100% of
the principal amount of such Debentures or (ii) the sum of the present values of
the remaining scheduled payments of principal and interest thereon (not
including the portion of any such payments of interest accrued as of the
redemption date) up to June 15, 2028, discounted, in each case, to the
redemption date on a semiannual basis (assuming a 360-day year consisting of
twelve 30-day months) at the Adjusted Treasury Rate (as defined below)
determined on the third Business Day preceding such redemption date, plus, in
each case, accrued and unpaid interest thereon to the redemption date.

          "Adjusted Treasury Rate" means, with respect to any redemption date,
the rate per annum equal to the semiannual equivalent yield to maturity of the
Comparable Treasury Issue, assuming a price for the Comparable Treasury Issue
(expressed as a percentage of its principal amount) equal to the Comparable
Treasury Price for such redemption date, plus (i) 0.00% for redemptions prior to
and including June 15, 2008 or (ii) 0.15% for redemptions from June 15, 2008 to
June 15, 2028.

          "Comparable Treasury Issue" means the United States Treasury security
selected by a Reference Treasury Dealer as having a maturity comparable to the
period from the redemption date to either June 15, 2008 or June 15, 2028, as
applicable, that would be utilized, at the time of selection and in accordance
with customary financial practice, in pricing new issues of corporate debt
securities of comparable maturity.

          "Comparable Treasury Price" means, with respect to any redemption
date, the average of
<PAGE>
 

the Reference Treasury Dealer Quotations for such redemption date.
"Reference Treasury Dealer Quotations" means, with respect to each Reference
Treasury Dealer and any redemption date, the average, as determined by the
Trustee, of the bid and asked prices for the Comparable Treasury Issue
(expressed in each case as a percentage of its principal amount) quoted in
writing to the Trustee by such Reference Treasury Dealer at 5:00 p.m. (New York
City time) on the third Business Day preceding such redemption date.

          "Reference Treasury Dealer" means each of Goldman, Sachs & Co.,
BancAmerica Robertson Stephens, and First Chicago Capital Markets, Inc. and
their respective successors; provided, however, that if any of the foregoing
shall cease to be a primary U.S. Government securities dealer (a "Primary
Treasury Dealer") or is no longer quoting prices for United States Treasury
securities, the Company shall substitute therefor another Primary Treasury
Dealer.

          In the event of redemption of this Security, in part only, a new
Security or Securities of this series and of like tenor for the unredeemed
portion hereof will be issued in the name of the Holder hereof upon the
cancellation hereof.

          This Security will be repaid on June 15, 2008, at the option of the
Holder, at 100% of its principal amount, together with accrued interest to June
15, 2008.  In order for a Holder to exercise this option, the Company must
receive at its office or agency in New York, New York, during the period
beginning on April 16, 2008 and ending at 5:00 P.M. (New York City time) on May
16, 2008 (or, if May 16, 2008 is not a Business Day, the next succeeding
Business Day), this Security with the form below entitled "Option to Elect
Repayment on June 15, 2008" duly completed.  Any such notice received by the
Company during the period beginning April 16, 2008 and ending at 5:00 P.M. (New
York City time) on May 16, 2008 (or, if May 16, 2008 is not a Business Day, the
next succeeding Business Day) shall be irrevocable.  No transfer or exchange of
this Security (or, in the event that this Security is to be repaid in part, such
portion of this Security to be repaid) will be permitted after such notice is
received by the Company.  The repayment option may be exercised by the Holder
for less than the entire principal amount of this Security, so long as the
principal amount that is to be repaid is equal to $1,000 or any integral
multiple thereof.  All questions as to the validity, form, eligibility
(including time of receipt) and acceptance of this Security for repayment will
be determined by the Company, whose determination will be final and binding.

          In the event of repayment of this Security, in part only, a new
Security or Securities of this series and of like tenor for the unrepayed
portion hereof will be issued in the name of the Holder hereof upon the
cancellation hereof.

          If an Event of Default with respect to Securities of this series shall
occur and be continuing, the principal of the Securities of this series may be
declared due and payable in the manner and with the effect provided in the
Indenture.
<PAGE>
 

          The Indenture contains provisions for defeasance at any time of the
entire indebtedness of this Security or certain restrictive covenants and the
related Events of Default with respect to this Security, in each case upon
compliance with certain conditions set forth therein.

          The Indenture permits, with certain exceptions as therein provided,
the amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Securities of each series to be
affected under the Indenture at any time by the Company and the Trustee with the
consent of the Holders of a majority in principal amount of the Securities at
the time Outstanding of each series to be affected. The Indenture also contains
provisions permitting the Holders of specified percentages in principal amount
of the Securities of each series at the time Outstanding, on behalf of the
Holders of all Securities of such series, to waive compliance by the Company
with certain provisions of the Indenture and certain past defaults under the
Indenture and their consequences. Any such consent or waiver by the Holder of
this Security shall be conclusive and binding upon such Holder and upon all
future Holders of this Security and of any Security issued upon the registration
of transfer hereof or in exchange herefor or in lieu hereof, whether or not
notation of such consent or waiver is made upon this Security.

          No reference herein to the Indenture and no provision of this Security
or of the Indenture shall alter or impair the obligation of the Company, which
is absolute and unconditional, to pay the principal of and any premium and
interest on this Security at the times, place and rate, and in the coin or
currency, herein prescribed.

          As provided in the Indenture and subject to certain limitations
therein set forth, the transfer of this Security is registerable in the Security
Register, upon surrender of this Security for registration of transfer at the
office or agency of the Company in any place where the principal of and any
premium and interest on this Security are payable, duly endorsed by, or
accompanied by a written instrument of transfer in form satisfactory to the
Company and the Security Registrar duly executed by, the Holder hereof or his
attorney duly authorized in writing, and thereupon one or more new Securities of
this series and of like tenor, of authorized denominations and for the same
Stated Maturity and aggregate principal amount, will be issued to the designated
transferee or transferees.

          The Securities of this series are issuable only in registered form
without coupons in denominations of $1,000 and any integral multiple thereof. As
provided in the Indenture and subject to certain limitations therein set forth,
Securities of this series are exchangeable for a like aggregate principal amount
of Securities of this series and of like tenor of a different authorized
denomination, as requested by the Holder surrendering the same.

          No service charge shall be made for any such registration of transfer
or exchange, but the Company may require payment of a sum sufficient to cover
any tax or other governmental charge payable in connection therewith.
<PAGE>
 

          Prior to due presentment of this Security for registration of
transfer, the Company, the Trustee and any agent of the Company or the Trustee
may treat the Person in whose name this Security is registered as the owner
hereof for all purposes, whether or not this Security be overdue, and neither
the Company, the Trustee nor any such agent shall be affected by notice to the
contrary.

          Interest on this Security shall be computed on the basis of a 360-day
year of twelve 30-day months.

          All terms used in this Security which are defined in the Indenture
shall have the meanings assigned to them in the Indenture.

          This Security shall be governed by and construed in accordance with
the laws of the State of New York without giving effect to the conflict of laws
provisions thereof.
<PAGE>
 

                  OPTION TO ELECT REPAYMENT ON JUNE 15, 2008


     The undersigned hereby irrevocably requests and instructs the Company to
repay the within or attached Security (or portion thereof specified below)
pursuant to its terms at a price equal to the principal amount thereof to be
repaid, together with interest thereon to June 15, 2008, to the undersigned at

--------------------------------------------------------------------------------

--------------------------------------------------------------------------------
(Please Print or Type Name, Address and Telephone Number of the undersigned)


     For the within or attached Security to be repaid, the Company must receive
at its office or agency in New York, New York, during the period beginning on
April 16, 2008 and ending at 5:00 P.M. (New York City time) on May 16, 2008 (or,
if May 16, 2008 is not a Business Day, the next succeeding Business Day) this
Security with this "Option to Elect Repayment on June 15, 2008" form duly
completed. Any such notice received by the Company during the period beginning
April 16, 2008 and ending at 5:00 P.M. (New York City time) on May 16, 2008 (or,
if May 16, 2008 is not a Business Day, the next succeeding Business Day) shall
be irrevocable. No transfer or exchange of this Security (or, in the event that
this Security is to be repaid in part, such portion of this Security to be
repaid) will be permitted after such notice is received by the Company.

     If less than the entire principal amount of the within or attached Security
is to be repaid, specify the portion thereof (which shall be $1,000 or an
integral multiple of $1,000) which the Holder elects to have repaid: $_________;
and specify the denomination or denominations (which shall be $1,000 or an
integral multiple of $1,000) of the Security or Securities to be issued to the
Holder for the portion of the within attached Security not being repaid (in the
absence of any such specification, one such Security shall be issued for the
portion not being repaid): $___________.


Dated:



                              --------------------------------------------------
                              Note: The signature to this Option to Elect
                              Repayment on June 15, 2008 must correspond with
                              the name as written upon the face of the Security
                              in every particular without alteration or
                              enlargement or any change whatsoever.