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The classical problem of diagnosability is discussed widely and the diagnosability of many well-known networks has been explored. We consider the diagnosability of a family of networks, called the matching composition network (MCN); a perfect matching connects two components. The diagnosability of MCN under the comparison model is shown to be one larger than that of the component, provided some connectivity constraints are satisfied. Applying our result, the diagnosability of the hypercube Qn, the crossed cube CQn, the twisted cube TQn, and the Mobius cube MQn can all proven to be n, for n≥4. In particular, we show that the diagnosability of the four-dimensional hypercube Q4 is 4, which is not previously known.