  We have extended the procedure to find the exact solution of the Riemann
problem in relativistic hydrodynamics to a particular case of relativistic
magnetohydrodynamics in which the magnetic field of the initial states is
tangential to the discontinuity and orthogonal to the flow velocity. The wave
pattern produced after the break up of the initial discontinuity is analogous
to the non--magnetic case and we show that the problem can be understood as a
purely relativistic hydrodynamical problem with a modified equation of state.
The new degree of freedom introduced by the non-zero component of the magnetic
field results in interesting effects consisting in the change of the wave
patterns for given initial thermodynamical states, in a similar way to the
effects arising from the introduction of tangential velocities. Secondly, when
the magnetic field dominates the thermodynamical pressure and energy, the wave
speeds approach the speed of light leading to fast shocks and fast and
arbitrarily thin rarefaction waves. Our approach is the first non-trivial exact
solution of a Riemann problem in relativistic magnetohydrodynamics and it can
also be of great interest to test numerical codes against known analytical or
exact solutions.
