  This study investigates the properties of waves in relativistic extended
magnetohydrodynamics (RXMHD), which includes Hall and electron thermal inertia
effects. We focus on the case when the electron temperature is
ultrarelativistic, and thus, the electron thermal inertia becomes finite at
near the proton inertial scale. We derive the linear dispersion relation of
RXMHD and find that the Hall and electron thermal inertia effects couple with
the displacement current, giving rise to three superluminous waves in addition
to the slow, fast, and Alfv\'en waves. We also show that the phase- and
group-velocity surfaces of fast and Alfv\'en waves are distorted by the Hall
and electron thermal inertia effects. There is a range of scales where the
group velocity of fast wave is smaller than that of the Alfv\'en and slow
waves. These findings are applicable to a region near the funnel base of
low-luminosity accretion flows where electrons can be ultrarelativistic.
