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This note gives a new graph-theoretic shape decomposition procedure, extending the idea in the paper ``Decomposition of Two-Dimensional Shapes by Graph-Theoretic Clustering'' by Shapiro and Haralick . A binary matrix is used in order to express the LI relation. A solution for the problems connected with artificial separation of two CS cliques and the presence of a regular concavity is proposed. Our algorithm produces nonoverlapping shape parts in much reduced execution time.