Group oriented (t, n) threshold digital signature schemes have a problem in that the underlying signature schemes will be broken if any t or more shadowholders conspire together with each other. This weakness was noted by Li et al. at Crypt'93, and later in 1994, they proposed a solution to this problem. However, their solution is impractical from the verifier's point of view. In fact, many people think that the verification period should be processed as quickly as possible since the message is signed just once but is verified many times. Besides the inefficiency of verification in Li et al.𠏋 scheme, Michels and Horster have also shown that the signer cannot be sure who his co-signers are in this scheme. Hence, impersonation in their solution is possible. To enhance security and promote the efficiency, we propose a new (t, n) threshold signature scheme.