The classic Bernstein mode instability driven by a perpendicular momentum ring distribution function is insensitive to the parallel distribution. However, in the relativistic treatment, owing to the inexorable coupling between the parallel and perpendicular momenta through the Lorentz factor, the parallel momentum distribution may affect the instability. This paper discusses such a problem by making use of a model parallel momentum distribution function. It is found that the parallel momentum spread only leads to the modification of the real frequency, but the instability growth rate is largely unaffected.