Fault diagnosis is one of the key topics in the study of computer program operation and automatic control of large complex systems these days. It can be used in wide-spanning areas. As early as the last century, researchers started to study diagnosis structures and made a series of progress. Moreover, the problem of diagnosability verification of a system received much attention from many researchers. Therefore, in this paper, a discrete event system (DES) is proposed and a diagnoser is constructed as an automaton model to verify the diagnosability of a given system. A method is proposed to test if a given system is diagnosable under the discrete event system structure. The states of a system are classified into three categories, and a diagnoser structure with basic algorithms and functions is defined to verify diagnosability. The proposed diagnoser structure can better capture the behavior of the system and verify its diagnosability.