  We calculate the relativistic thermal bremsstrahlung Gaunt factor for the
high-temperature plasma which exists in clusters of galaxies. We calculate the
Gaunt factor by employing the Bethe-Heitler cross section corrected by the
Elwert factor. We also calculate the Gaunt factor by using the
Coulomb-distorted wave functions for nonrelativistic electrons following the
method of Karzas and Latter. By comparing the Gaunt factors calculated by these
two different methods, we carefully assess the accuracy of the calculation. We
present the numerical results in the form of tables.
