  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. We present a systematic method for the inclusion
of the multiple scattering effects. The multiple scattering contribution is
found to be very small compared with the single scattering contribution. For
high-temperature galaxy clusters of k_{B}T_{e} = 15keV, the ratio of the both
contributions is -0.3% 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.
