Group signature schemes allow a group member to sign messages anonymously on behalf of the group. In case of dispute, only a designated group manager can reveal the identity of the member. During last decade, group signature schemes have been intensively investigated in the literature and applied to various applications. However, there has been no scheme properly handling the situation that a group member wants to leave a group or is excluded by a group manager. As noted in[3], the complexity of member deletion stands in the way of real world applications of group signatures and the member deletion problem has been a pressing open problem. In this paper we propose an efficient group signature scheme that allows member deletion. The length of the group public key and the size of signatures all independent of the size of the group and the security of the scheme relies on the RSA assumption. In addition, the method of tracing all signatures of a specific member is introduced.