In 1998, an efficient group signature scheme (the Lee-Chang scheme) was proposed, based on the discrete logarithm problem. In this scheme, different group signatures of a signer for different messages contain some identical information. Once one group signature is identified, all previous group signatures are also identified at the same time. This is impractical for applications of group signatures. The authors propose an improvement on the Lee-Chang scheme to solve the above problem. The improved group signature scheme preserves the main merits inherent in most of the Lee-Chang scheme. The security of the improved scheme is also based on the discrete logarithm problem.