A new graph partitioning algorithm for use on structurally unsymmetric systems is presented. Unlike other partitioning algorithms that have been used to provide reorderings for structurally symmetric matrices, this algorithm employs a bipartite graph model, and hence, can be used to consider unsymmetric permutations of structurally unsymmetric matrices. It is shown that the algorithm can be used in identifying coarse-granular, balanced tasks in the direct solution of flowsheeting matrices by parallel techniques based on generalized block-tridiagonal and nested-block-tridiagonal matrix structures. It is also shown that such reorderings can be obtained inexpensively, in worst-case running times that increase linearly with the order of the matrix.