Comparison-based system-level fault diagnosis is attractive alternative to test-based fault diagnosis. The MM* comparison model assumes that every processor in the system to be diagnosed makes a comparison between the responses of any two processors with which it can communicate directly to the same system tasks. Due to many excellent properties, hypercube structures have become popular choices for interconnection network topology of real multiprocessor systems. Sengupta and Dahbura proposed a diagnosis algorithm for general diagnosable systems under the MM* model, with O(N⁵) time complexity, where N is the number of processors in the system. In this paper, we propose a fault diagnosis algorithm for hypercube systems under the MM* model by exploiting cycle decomposition properties of hypercube. Based on judiciously designed data structures, this diagnosis algorithm can achieve 0(N\log _2^2 N) time complexity, which is linear in the size of input. Therefore, the new diagnosis algorithm is significantly superior to Sengupta-Dahbura?s for hypercube systems.