A new boundary condition treatment strategy is presented in this research for solving the twodimensional inviscid internal flow problems, spatial discretization has made by finite difference formulation using flux vector splitting of Van Leer. The time advancement is made using Euler backward time stepping technique. The aim of this research is to present new non-reflecting boundary condition treatment in the cases of metaphysical flow conditions occurred at the same space point. Such situation occurred in the internal flow problems as the corner points in nozzle., numerical flow simulations is carried out and shows good agreement with the analytical values and with published data.