Recently, some quantum blind signature protocols have been proposed. However, the previous schemes cannot satisfy the unlinkability requirement. To overcome the drawback of unlinkability in the previous schemes, we propose a new quantum blind signature based on Bell states with the help of an authentic party. In this paper, we provide a method to inject a randomizing factor into a message when it is signed by the signer and then get rid of the blind factor from the blinded signature when it is verified by the verifier. Even when the message owner publishes the message-signature pair, the signer cannot identify the association between the message-signature pair and the blind signature he generated. Therefore, our scheme really realizes unlinkability property. At last, analysis results show that this scheme satisfies the basis security requirements of a weak signature such as no-counterfeiting, no-disavowing, blindness and traceability, and our total efficiency is not less than the previous schemes.