The design of cell formation includes the formation of machine cells and part family assignment to each cell. The cell formation is considered as a most critical step in a cellular manufacturing system. This paper proposes a technique for the formation of machine cells and part families with the objective of minimising the exceptional elements using graph decomposition of a bipartite graph into near complete bipartite graph. In the proposed algorithm known as graph decomposition algorithm, the machines and parts are considered as vertices and the links between machines and parts are edges. This approach is found to offer reliable and better solutions when compared to earlier approaches available in the literature.