  The spectral distortion of the cosmic background radiation produced by the
inverse Compton scattering on hot electrons in clusters of galaxies (thermal
Sunyaev-Zeldovich effect) is calculated for arbitrary optical depth and
electron temperature. The distortion is found by a numerical solution of the
exact Boltzmann equation for the photon distribution function. In the limit of
small optical depth and low electron temperature our results confirm the
previous analyses. In the opposite limits, our method is the only one that
permits to make accurate calculations.
