Abstract: A new trnsonic relaxation method is presented which can be used for computation of transonic,potential flows through two-dimensional cascade with large camber angle.A non-orthogonal mesh system composed of streamlines and straight lines parallel to y-axis is employed here.The governing equation expressed by the streamline coordinate system is solved in physical plane.Because of the streamline coordiate system,the governing equation is greatly simplified and the formulation of the finite difference scheme is also made correctly and easily.In the case of the cascade with large camber angle (especially for turbine) direct formulation of difference scheme from full-potential equation (instead of perturbation-potential equation) is suggested. The numerical experimentations show that both the convergence and the stability of the finite difference scheme proposed here are satisfactory.The compuation results with acceptable accuracy can be obtained after 60 to 90 relaxation steps.The numerical examples also show that the results are in good agreement with experimental data and analytical solution (for Hobson-airfoil).