  This Letter presents a magnetohydrodynamic model that describes the
small-amplitude fluctuations with wavelengths comparable to ion inertial length
in the presence of a relativistically strong mean magnetic field.
  The set of derived equations is virtually identical to the non-relativistic
Hall reduced magnetohydrodynamics (Schekochihin et al. 2019), differing only by
a few constants that take into account the relativistic corrections.
  This means that all the properties of kinetic Alfv\'en turbulence and ion
cyclotron turbulence inherent in the non-relativistic Hall regime persist
unchanged even in a magnetically dominated regime.
