The stability analysis of a finite-amplitude wave solution of the generalized Landau equation due to Stuart and DiPrima (1978) is extended. For a given supercritical stability parameter, a finite-amplitude wave of wavenumber ko is stable if ko satisfies -S(k₁-k_c)<k0-k_c<S(k₂-k_c), where k₁ and k₂ are the wavenumbers of the neutral waves, kc the wavenumber of the neutral wave at the marginally stable state. It is shown that S is a function of only two real quantities, the amplitude dispersion factor d and the wavenumber dispersion factor l, which, in turn, are functions of the coefficients of the generalized Landau equation. The functional form of S(d, l) is completely determined, so that the value of S is calculated for all possible values of the coefficients of the generalized Landau equation.