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The first step in the diagnosis of failure occurrences in discrete event systems is the verification of the system diagnosability. Several works have addressed this problem using either diagnosers or verifiers for both centralized and decentralized architectures. In this technical note, we propose a new algorithm to verify decentralized diagnosability of discrete event systems. The proposed algorithm requires polynomial time in the number of states and events of the system and has lower computational complexity than all other methods found in the literature. In addition, it can also be applied to the centralized case.