In this paper, an approach is developed for diagnosability analysis of discrete event systems (DESs) modeled by labeled Petri nets (LPNs). Our approach, which extends from the on-the-fly and incremental diagnosis technique, aims at improving the efficiency of diagnosability analysis by generating as less state space as possible. Thanks to the minimal explanation notion, our improved approach holds the existing advantages of on-the-fly technique, while generating less fault markings (FMs).