  We study the free boundary problem for a contact discontinuity for the system
of relativistic magnetohydrodynamics. A surface of contact discontinuity is a
characteristic of this system with no flow across the discontinuity for which
the pressure, the velocity and the magnetic field are continuous whereas the
density, the entropy and the temperature may have a jump. For the
two-dimensional case, we prove the local-in-time existence in Sobolev spaces of
a unique solution of the free boundary problem provided that the
Rayleigh--Taylor sign condition on the jump of the normal derivative of the
pressure is satisfied at each point of the initial discontinuity.
