The efficiency of solving sparse linear systems on parallel proceesors and more complex multicluter architecture such as cedax is greatly enhanced if relatively large grain computational tasks can be assignet to each cluster or processor. The ordering of a system into a borderd block upper triangular form facilites a ressonable large-grain partitioning. A New algorithm wich produces this form for unsymmetric sparse linear systems is considered and the factorisation algorithm is presented . Computational results are presented for the cedax multiprocessor