Abstract: On the basis of two steps explicit methods,author investigates the application of the theory of Flux Vector Splitting(FVS)of J.L.Steger and R.F.Warming.Besides the simplified split flux vector formula,a new explicit scheme is proposed for solving hyperbolic differential equatione.It is a explicit two steps FVS scheme of second order accuracy.At first it was compared with MacCormack's scheme issued in 1972(MC72)in numerical computation.And finally a 2-D flow of a rectangular nozzle with its jet plume was analysed numerically by the present scheme.The results indicate some high performances of the present scheme:1.Numerical vibrations near the front surface of shock waves vanish.2.The scheme runs without artificial viscosity.3.It takes just as much time as MC72 takes to solve a flow field.The scheme features the higher inherent viscosity of the scheme compared with that of MC72.