We propose an undeniable (t, n) threshold signature scheme with cheater identification. The proposed scheme has the following features: (1) no trusted third party is required for key generation; (2) no additional interactive protocol is required for the generation of the group's public key; (3) anytmembers can cooperatively sign a message with the assistance of a secure cryptographic module designated by hardware; and (4) the verifier can verify the group signature by only knowing the group's public key; it is not necessary to know the participating signers involved. The proposed scheme also provides capabilities against cheating tricks plotted by signers in the key generation and group signature generation phases.