Recently, Hwang and Li proposed a remote user authentication scheme that does not require a password table to verify the legitimacy of a legal user. 1 This method uses smart cards. To benefit from this advantage, other research works have explored adding such features as reducing the computational cost, adopting userfriendly passwords, making it easier to change user passwords, etc. However, as cryptanalysis has evolved, a series of modifications that improve the known security flaws have been made subsequently. This article deals with a security problem found in a latest modification and improves it in order to construct a more secure function. The article also highlights a feature, mutual authentication between a server and users, found in many authentication protocols but seldom found in the considered series of modifications.