  We present an accurate analytic fitting formula for the numerical results for
the relativistic corrections to the thermal Sunyaev-Zel'dovich effect for
clusters of galaxies. The numerical results for the relativistic corrections
have been obtained by numerical integration of the collision term of the
Boltzmann equation. The fitting is carried out for the ranges 0.02 < theta_{e}
< 0.05 and 0 < X < 20, where theta_{e} = k_{B}T_{e}/m_{e}c^{2}, X =
omega/k_{B}T_{0}, T_{e} is the electron temperature, omega is the angular
frequency of the photon, and T_{0} is the temperature of the cosmic microwave
background radiation. The accuracy of the fitting is generally better than
0.1%. The present analytic fitting formula will be useful for the analyses of
the thermal Sunyaev-Zel'dovich effect for high-temperature galaxy clusters.
