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Hwang and Li (see IEEE Trans. Consumer Electron., vol.46, no.1, p.28-30, 2000) proposed a new remote authentication scheme using smart cards. Their scheme is based on the ElGamal's public key cryptosystem. However, Chan and Cheng (see IEEE Trans. Consumer Electron., vol.46, p.992-993, 2000) pointed out that the scheme is vulnerable to the masquerade attack. In this article, we show a different attack on Hwang-Li scheme which is easier and simpler. Furthermore, we present an enhanced scheme for repairing the above attacks.