A fourth order semi compact finite difference scheme has been developed to solve unsteady incompressible Navier-Stokes equations in stream function and vorticity formulation. The governing equations are transformed into curvilinear coordinates using body fitted coordinate system to enable the developed scheme to handle non-regular domains. Two test problems are utilized to explore the efficiency of the scheme. It is found that the solutions obtained with the present scheme are in good agreement with the analytical results or with the existing results depending on the availability. © Springer-Verlag 2005.