  We extend the formalism for the calculation of the relativistic corrections
to the Sunyaev-Zel'dovich effect for clusters of galaxies and include the
multiple scattering effects in the isotropic approximation. We present the
results of the calculations by the Fokker-Planck expansion method as well as by
the direct numerical integration of the collision term of the Boltzmann
equation. The multiple scattering contribution is found to be very small
compared with the single scattering contribution. For high-temperature galaxy
clusters of kT=15keV, the ratio of the both contributions is -0.2% in the Wien
region. In the Rayleigh--Jeans region the ratio is -0.03%. Therefore the
multiple scattering contribution is safely neglected for the observed galaxy
clusters.
