A smart card based scheme is very practical to authenticate remote users. In 2004, Juang [Juang WS. Efficient password authenticated key agreement using smart cards. Computers and Security 2004;23:167-73] proposed a mutual authentication scheme using smart cards. The advantages in the scheme include freely chosen passwords, no verification tables, low communication and computation cost, and session key agreement. In addition, synchronized clocks are not required in the scheme due to its nonce based approach. In this paper, however, we shall discuss the weakness of Juang's [Juang WS. Efficient password authenticated key agreement using smart cards. Computers and Security 2004;23:167-73] scheme and propose another similar scheme to improve the weakness. Our scheme not only preserves all the advantages of Juang's scheme but also improves its efficiency. (C) 2005 Elsevier Ltd. All rights reserved.