The paper deals with the definition of procedure that enables one to determine, for a given plant, if all faults can be detected and located after a finite sequence of observable events. More formally, the diagnosability is the property that every fault can be correctly detected from the observable events of the system after its occurrence no later than a bounded number of events. In this paper, the diagnosability problem of Discrete Event Systems (DESs) is studied. As modeling tool, finite-state automaton in an event-based framework is used. A necessary and sufficient condition of diagnosability of such systems is proposed. The results proposed in this paper allow checking the diagnosability of discrete event systems in an efficient way, i.e. in polynomial time.