Some privacy-protecting electronic payment systems [2],[13], [15],[17] have been proposedto realize the revocable anonymity among users. In this paper, organizing all users into a group, we present a new fair off-line electronic cash system (E-Cash for short). This new E-Cash system is more efficient andmore secure. The system is able of coin tracing ando wner tracing. The anonymity of the system can be revocable under certain conditions by an off-line trusted third authority, the system is untraceable (under normal cases), unlinkable and double-spending resistant. Furthermore, compared with the previous E-Cash systems, our payment protocol is more efficient in computing.