A system is t-diagnosable if all faulty nodes can be identified without replacement when the number of faults does not exceed t, where t is some positive integer. Furthermore, a system is strongly t-diagnosable if it is t-diagnosable and can achieve (t+1)-diagnosable except for the case where a node's neighbors are all faulty. In this paper, we propose some conditions for verifying whether a class of interconnection networks, called matching composition networks (MCNs), are strongly diagnosable under the comparison diagnosis model.