Extraordinary and quasilongitudinal waves propagating at an arbitrary angle with respect to the steady magnetic field are investigated within the fully relativistic theory. The results of the present paper complement the previously reported results obtained within the weakly relativistic approximation by new effects which are brought on by finite -values and by relativistic effects at high electron temperatures. In particular, it is found that in a wide -range relativistic effects lead to an important increase of the right-hand cut-off density. The phenomenon of mode interaction is examined in detail, in particular its and temperature dependence. It is found that there are three points at which the solutions of the fully relativistic dispersion equation describing the extraordinary and the least damped quasilongitudinal modes coincide. The first branch point occurs at low plasma densities, near the fundamental electron cyclotron (EC) frequency. It may be located on both, the high- and low-density side of the high-field limit of the right-hand cut-off. The remaining two branch points form a closed region in the parameter space in which mode interaction occurs. At low electron temperatures, the range of frequency variation of the aforementioned region is very narrow and centred very close to the second EC harmonic. The increase of the electron temperature enlarges the -range in which mode interaction occurs appreciably. The fact that mode interaction occurs at relatively large -values should be taken into account when considering the EC absorption and emission.