We revisit the notion of the anonymous signature, first formalized by Yang, Wong, Deng and Wang , and then further developed by Fischlin  and Zhang and Imai . We present a new formalism of anonymous signature, where instead of the message, a part of the signature is withheld to maintain anonymity. We introduce the notion unpretendability to guarantee infeasibility for someone other than the correct signer to pretend authorship of the message and signature. Our definition retains applicability for all previous applications of the anonymous signature, provides stronger security, and is conceptually simpler. We give a generic construction from any ordinary signature scheme, and also show that the short signature scheme by Boneh and Boyen  can be naturally regarded as such a secure anonymous signature scheme according to our formalism.