The viscous incompressible fluid flow in a channel with a step is studied under steady state conditions. An earlier work [3] employed a fourth order scheme with second order boundary conditions to obtain very accurate results which were in close agreement with various other studies in channel flow problems. The present work employs a fifth order scheme using 13-point grid. Moreover, it uses fourth order boundary conditions to further improve the accuracy of results. Two well-known workshop problems are chosen for the comparison of results, the problems of contraction and expansion flows. The results compare favorably with the literature from experimental and numerical view-point.