This research is concerned with Machine-Part Group Formation(MPGF) methodology for Flexible Manufacturing Systems(FMS). The purpose of the research is to develop a new heuristic algorithm for effectively solving MPGF problem. The new algorithm is proposed and evaluated by 100 machine-part incidence matrices generated. The performance measures are (1) grouping ability of mutually exclusive block-diagonal form. (2) number of unit group and exceptional elements, and (3) grouping time. The new heuristic algorithm has the following characteristics to effectively conduct MPGF : (a) The mathematical model is presented for rapid forming the proper number of unit groups and grouping mutually exclusive block-diagonal form, (b) The simple and effective mathematical analysis method of Rank Order Clustering(ROC) algorithm is applied to minimize intra-group journeys in each group and exceptional elements in the whole group. The results are compared with those from Expert System(ES) algorithm and ROC algorithm. The results show that the new algorithm always gives the group of mutually exclusive block-diagonal form and better results(85%) than ES algorithm and ROC algorithm.