The problem of secure and efficient revocation of membership without incurring big costs has been considered, but no satisfactory solution was reported. This paper proposes a new revocation method of membership based on the ACJT group scheme. The solution is efficient in that it only needs one multiplication to update the public key for the group manager to exclude one group member, and the signing and verifying procedure is independent of the number of the current and excluded group members. To the best of our knowledge, the signing and verifying procedure in the existing revocation schemes is dependent on the number of either the current or the excluded group members, and thus the group manager needs a heavy computation load to update the public key.