This paper addresses the problem of grouping machines in order to design cellular manufacturing ceils, with an objective to minimize inter-cell flow. This problem is related to one of the major aims of group technology (GT): to decompose the manufacturing system into manufacturing cells that are as independent as possible. This problem is NP-hard. Thus, nonheuristic methods cannot address problems of typical industrial dimensions because they would require exorbitant amounts of computing time, while fast heuristic methods may suffer from poor solution quality. We present a branch-and-bound statespace search algorithm that attempts to overcome both these deficiencies. One of the major strengths of this algorithm is its efficient branching and search strategy. In addition, the algorithm employs the fast Inter-Cell Traffic Minimization Method to provide good upper bounds, and computes lower bounds based on a relaxation of merging.