The numerical method presented by Safaiy et al.  is reformulated with Finite Volume method in its most general form and tested on non-orthogonal flow problems. Navier-Stokes equations are solved for the solution of stream function and Vorticity. Numerical solutions of the driven skewed cavity flow, solved using a fine grid (513×513) mesh, are presented for Reynolds number of 100 and 1000 for skew angles ranging between . The results are compared with the numerical solutions found in the literature and also with analytical solutions as well.