Most of systems used in real fields are considered as multistate systems with multistate components. As one of methods for performance evaluation of the system, reliability analysis has been popularly used. In this paper, we propose an improved reliability analysis method which is based on state space decomposition method of Aven (1985). In deriving upper bounds, our method uses sets of unspecified states whereas Aven (1985) excludes sets of unacceptance states. Also, closer lower bounds to an exact reliability are obtained by considering of importance of min-path vectors.