As a continuation of our previous work on the (stable) local modes and their effect on the absorption band width of isolated impurity centres, the problem of unstable local modes is considered in this article. By means of the method of group theory, both the unstable local modes and the scattered wave are classified according to the irreducible representations of relevant site group. The case of a simple cubic lattice with nearest neighbour interaction is discussed in detail and the related calculations are carried out. The results show that when a g-type unstable local mode has a rather narrow width, its contribution to the absorption band width may become so large that it exceeds the total contribution of all other lattice vibration waves. Finally, a brief discussion is given on the microscopic basis of the empirical formula of a "single effective frequency" of the electron-phonon coupling.