Clustering systems can discover intentional structures in data and extract new knowledge from a database. Many incremental and nonincremental clustering algorithms have been proposed, but they have some problems. Incremental algorithms work very efficiently, but their performance is strongly affected by the input order of instances. On the other hand, non-incremental algorithms are independent of the input order of instances but often take a long time to build clusters for a large database. Moreover, most of incremental and non-incremental algorithms build concept hierarchies with single inheritance. Many real world problems require different points of view to be solved. Concept hierarchies with multiple inheritances are useful for such problems. We propose a non-incremental and efficient algorithm which builds concept hierarchies with multiple inheritances.