[en] Using kinetic theory, new dispersion relations based on relativistic Maxwellian velocity distribution are obtained for ordinary and extraordinary modes in a strongly magnetized hot plasma. It is observed that, unlike the non-relativistic Maxwellian distribution case where only real dispersion relation appears for the relativistic case both the real dispersion relations and the damping decrements occur. To illustrate the results graphically, we have plotted the phase velocity squared and the growth rate versus frequency for different values of n. For O-mode, the non-propagation region disappears as we increase the values of the harmonic number n while for the X-mode, the propagation region occurs only for the large harmonics. As regards damping, for O-mode the damping rate is small for small n and increases with n. For X-mode, on the contrary, the damping rate decreases as n increases