Abstract: To ensure the correctness and uniqueness of the diagnosis, the definition of diagnosability is presented and an algorithm is proposed to test the diagnosability of Higher-order Discrete Event Systems (HDES). To diagnose HDES, it is needed to construct a diagnosis engine of HDES, which is also used for testing the diagnosability. The state of diagnosis engine includes sets of faults, thus, it is not necessary to traverse the whole graph to search faults when the behavior has been reconstructed. Furthermore, in the premise of no influence on the diagnosis results, the transition between states is constrained, thus, to avoid the generation of unnecessary nodes.