A (t,n) threshold signature scheme allows n members of a group to share a secret key such that any t members can create a valid group signature. Of course, any t members can compromise this system. However designing a (t,n) threshold signature scheme based on the Digital Signature Standard (DSS) is difficult if there is no trusted party to distribute the shares of the secret. Langford (1995) proposed a (t/sup 2/-t+1)-out-of-n threshold DSS signature scheme without a trusted party. It requires t/sup 2/-t+1 members to sign a document, but t members can conspire to destroy this scheme. Gennaro et al. (1996) improved that result by proposing a robust threshold DSS signature scheme which requires 2t+1 members in the signing procedure. This paper proposes a new method to reduce the number of signers to t+1. We also extend our scheme to a generalized case.