Abstract: In this paper the upwind factor method is extended to treating the two-dimensional transonic flows. The Navier Stokes equations with k-e turbulence model are discretized in a non orthogonal body-fitted coordinate system, and the upwind factor method is employed to ensure the numerical stability of the scheme. The maximum local time step is determined by the criterion that the cofficients in discretized equations must be non-negative.The numerical experiments are carried out for DFVLR transonic cascade for inlet Mach number of 0. 82 and 1. 05. and numerical results are compared with the experimental data in good agreement. Also, the numerical results are compared with the results calculated with a four stage Range Kutta time stepping scheme of an Euler code.