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Clustering of large-scale binary matrices requires a considerable computational effort. In some cases this effort is lost since the matrix is not decomposable into mutually separable submatrices. A cluster identification algorithm which has relatively low computational time complexity O(2mn) is developed. It allows checking for the existence of clusters and determines the number of mutually separable clusters. A modified cluster identification algorithm for clustering nondiagonally structured matrices is also presented. The two algorithms are illustrated in numerical examples.