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