Auroral kilometric radiation (AKR) is known to be produced in a region in which the plasma sheet electrons have speeds v2/c2> &ohgr;p2/&OHgr;e2≪1. Under such conditions, relativistic effects on the dispersion of extraordinary-mode waves near the electron cyclotron frequency are found to be very significant. Linear theory and computer simulation applied to a model distribution indicate that a k∥=0 extraordinary mode with Re &ohgr;≲&OHgr;e dominates the radiation emission resulting from the cyclotron maser instability. These results suggest that the hot electrons determine the propagation characteristics of AKR and that larger growth rates are possible for direct amplification of extraordinary waves in the auroral region than predicted by calculations using cold-plasma dispersion.