The multifrontal method known for solving linear algebraic systems with symmetric sparse matrices has been adapted for the systems whose matrices possess an irregular sparsity. The new method enables to use BLAS 2 and BLAS 3 routines which makes it attractive also for parallel and vector supercomputers. Computational experiments performed on a CRAY C-98 show a satisfactory performance gain of the new method when compared to the classical multifrontal and other unsymmetric linear system solvers.