Unforgeability and blindness are two important properties of blind signature. The latter means that after interacting with various users, the signer is unable to link a valid message-signature pair. In ICCSA 2006, Zhang et al. showed that a signer in an identity-based blind signature scheme proposed by Huang et al. is able to link a valid messagesignature pair obtained by some user. They also presented an improved scheme to overcome this flaw. In ICICIC 2006, Zhang and Zou showed that the identity-based blind signature scheme proposed by Zhang and Kim also suffered from the similar linkability attack. In this paper, we first show that the so-called linkability can be shown for Zhang et al.’s improved scheme as well. We then point out that the linkability attack against the Huang et al. scheme and the Zhang-Kim scheme is invalid.