Summary: A limit is given for the Mach number above which there is a qualitative change in the properties of the unstable mode of characteristic oscillations of the boundary layer from the case of an incompressible fluid. Consequently, the compressibility of a gas has a maximum growth increment in the neighbourhood of the upper branch of the neutral curve, which might not only be greater than the local maximum in the neighbourhood of the lower branch, but even be a different order of magnitude. An example is given where the function which describes the upper branch of the neutral curve becomes triple-valued. Under the given condition there are four neutral values of the wave number corresponding to a fixed Reynolds number, and the domain of instability splits into two.