Abstract: A threshold digital signature scheme is proposed by Fei Ru-chun and Wang Li-na.Its security is based on the difficulty of solving discrete logarithm in finite field and quadratic residue on some special conditions.The method is constructed to find out the malicious shareholders who disrupt the signature process and forges.Based on number theory，the authors firstly show there are some insufficiencies and potential hazard in the scheme proposed by Fei，et al.That is to say，any t members cannot impersonate another set of group members to sign any message withstand conspiracy attack.Secondly，the authors also propose a new scheme using the idea of Williams to solve the above questions.Compared to the existing threshold signature schemes，the scheme needs not to renew the members’ shadows when the system has renewed and the verification is easy.