  A method to derive stationary solutions of the relativistic Vlasov-Maxwell
system is explored. In the non-relativistic case, a method using the Hermite
polynomial series to describe the deviation from the Maxwell-Boltzmann
distribution is found to be successful in deriving a few stationary solutions
including two dimensional one. Instead of the Hermite polynomial series, two
special orthogonal polynomial series, which are appropriate to expand the
deviation from the Maxwell-J\"uttner distribution, are introduced in this
paper. By applying this method, a new two-dimensional equilibrium is derived,
which may provide an initial setup for investigations of three-dimensional
relativistic collisionless reconnection of magnetic fields.
