MacCormack′s flux splitting method has proven itself guite fast converging in numerical simulation of flows in converging-diverging nozzle.In this paper a development on the basis of this method is presented for Euler equations in order to obtain numerical solutions of inviscid transonic flow through a two-dimensional turbine cascade.In the present finite-area flux splitting implicit method the Gauss-Seidel line relaxation recommended by R.W.MacCormack is applied to solving the implicit descretization equations.But we abandon the predictor-corrector two-step method to cut down the computational time in every time-step

because it cannot enhance the accuracy of the steady soluton in flux-splitting methods.In our practical computation

in order to improve the accuracy of the solution

the right side of the difference equation is discretized to be of second order accuracy

the blade wall boundary conditions and the numerical results show that the present method retains the effective convergence rate (only about 30 timesteps to attain a steady solution)and yield numerical solutions conformable with the experimental results.