The key issue in e-commerce security is digital signature. Chaum fisrtly proposed the concept of blind digital signature, and designed an untraceable payments. To avoid threats from chosen-message attacks presented by Coron, Naccache and Stern at Crypto?99, Fan et al. proposed a randomization enhanced Chaum?s blind signature scheme, by injecting a random factor into messages. In this paper, we first formally define the unlinkability of blind signature scheme. According to this definition, we prove that Fan?s scheme does not possess the unlinkablity property: after the message and signature have been revealed to the public by the sender, the signer can trace the corresponding blinded message and signature by constructing a linkage between the message and the blinded message. Therefore, Fan?s scheme cannot provide true blind signatures.