A ring signature or a witness-indistinguishable signature is a setup-free group signature with no group manager. Defined by a set of public keys, a group is created spontaneously without any group member's collaboration or awareness. It allows members of the group to sign messages on behalf of the group without revealing their identities (signer anonymity). Since there is no group manager, no one can revoke the identities of the signers. In this paper, we point out that a ring signature scheme proposed by Abe, Ohkubo and Suzuki in ASIACRYPT'2002, is not signer anonymous. We also note that the authors' full paper version in IEICE Transaction Fundamentals contains a different version that defends against our attack. However, the full-paper version is more difficult to implement and is less efficient. We propose a different approach to fix the problem and show that our modification does not degrade the performance of the original scheme and is easier to implement than their full-paper version.