Contrary to the parallel flow approach most often studied, the growth rates of unstable waves of the supersonic mixing layer are analyzed with the consideration of flow nonparallelism by employing the method of multiple scales. Flow parameters including Reynolds number, Mach number, velocity ratios and temperature ratios influencing on the instability‐wave solutions are investigated. The mean flow is determined by solving the compressible boundary layer equations and applying the Sutherland law relating the viscosity to the temperature. In this work, two dimensional compressible stability equations are solved to secure the spatial growth rate of instability waves of the flow.