  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. The calculations in this paper are made for the fully ionized
plasma for the following cases: Z = 10 (Ne), 12 (Mg), 14 (Si), 16 (S), 26 (Fe).
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.
