Abstract: In 1998, Lee and Chang proposed a group signature scheme based on the discrete logarithm problem. However, their scheme lacks unlinkability: once one group signature is identified, all the previous signatures made by the same signer are also identified. To solve this problem, Tseng and Jan gave an improved scheme, which was proved still linkable by Sun. Moreover, Joye, Lee and Hwang pointed out that there was a fatal error in the security of the Lee Chang group signature scheme and its derivatives （including Tseng Chang scheme）. Later, Tseng and Jan made a modification of their previous schemes. Although compensating this security leak and making Sun’s linkage attack unavailable, an important property, verifiability, is lost. In the case of a dispute, the group authority can identify the signer, but he/she is unable to convince other verifiers about that. In this paper, a quasi formal definition of group signature is presented and a new implementation scheme is given based on Tseng and Jan’s two schemes in addition. simple analysis is also made of the new scheme.