Computer simulation of complex chemical processes is increasingly being used in the design optimization and control of chemical facilities. Industrial-scale modeling involves the solution of large systems of algebraic differential equations. This is very computationally intensive with a large part of the computing time attributed to the repeated solution of large, sparse, unsymmetric systems of linear equations. One way of speeding up the simulation is to solve the linear systems efficiently in parallel by reordering the unsymmetric matrices into a bordered block-diagonal (BBD) form. In this paper a multilevel ordering algorithm is presented. A multilevel technique, which provides a global view, is combined with a Kernighan-Lin algorithm to form an effective unsymmetric matrix ordering algorithm MONET (Matrix Ordering for minimal NET-cut). Numerical results confirm that this algorithm gives ordering of better quality than existing algorithms.