The plane-wave propagation can be generalized as a definite-solution problem of one-dimensional wave equation. In spite of the simple formality

solutions of one-dimensional wave equation in inhomogeneous media have to be solved with the aid of numerical methods. The classic three-level five-point finite difference scheme is a usual numerical method to calculate partial differential equations

which must meet the stable condition as an explicit iteration method. The stable condition is

where is wave velocity

is time sample interval

and is space sample interval. When or

the finite difference scheme is just up to the critical stable state. In such a case a space sample interval just equals wave propagation distance in a time sample interval

so the classic difference scheme exactly expresses plane-wave propagation theory and can be used to obtain exact solutions of one-dimensional wave equations. However

because of existence of wave impedance interfaces

the algorithm is unable to calculate wave fields in heterogeneous layer media. In order that the classic difference scheme in the critical stable state can be generalized to apply to heterogeneous layer media

an improved scheme is put forward

which can deal with impedance interfaces. Its stable condition is also given by Fourier transform analysis and the correctness is proved by some numerical model tests.