In 2010, Yeh et al. proposed two robust remote user authentication schemes using smart cards; their claims were such that their schemes defended against ID-theft attacks, reply attacks, undetectable on-line password guessing attacks, off-line password guessing attacks, user impersonation attack, server counterfeit attack and man-in-the-middle attack. In this paper, we show that Yeh et al.’s schemes are still vulnerable to ID-theft attack, off-line password guessing attacks, undetectable on-line password guessing attacks and user impersonation attack. Notably, problems remain in situations where the user lost a smart card or the malicious legal user. To remedy these flaws, this paper proposes an improvement on Yeh et al.’s remote user authentication schemes using smart cards.