A blind signature scheme is a protocol for obtaining a digital signature from a signer, but the signer can neither learn the messages he/she sign nor the signatures the signature requesters obtain afterwards. A partially blind signature scheme is a variant such that part of the message contains pre-agreed information (agreed by the signer and the signature requester) in unblinded form, which can be viewed as a cross between the traditional digital signature and the blind signature. A restrictive blind signature scheme is a protocol that allows a signature requester to obtain a blind signature on a message from a signer, but the choice of message is restricted and must conform to certain rules. A restrictive partially blind signature scheme incorporates the advantages of the partially blind signature scheme and of the restrictive blind signature scheme. In this paper, a flaw in the Huang-Chen-Kou's untraceable partially blind signature scheme by Huang, Z. et al, (2004) is pointed out, and a new and simpler restrictive partially blind signature scheme is proposed, which can be applied in the design of efficient fair electronic cash scheme