System-level diagnosis aims to identify faulty processors in a multiprocessor system by means of analyzing the test results among the processors. (t, k)-Diagnosis, which is one of the most important system-level diagnosis strategies, requires at least k faulty processors identified in each iteration provided there are at most t faulty processors, where t >= k. In this paper, a new (t, k)-diagnosis algorithm for regular networks is proposed. Experimental results show that the proposed algorithm has larger values of t for tori and matching composition networks, in comparison with previous (t, k)-diagnosis algorithms.