  A third order shock-capturing numerical scheme for three-dimensional special
relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against
several numerical tests. The simple and efficient central scheme described in
Paper I (Del Zanna and Bucciantini, Astron. Astrophys., 390, 1177--1186, 2002)
for relativistic hydrodynamics is here extended to the magnetic case by
following the strategies prescribed for classical MHD by Londrillo and Del
Zanna (Astrophys. J., 530, 508--524, 2000). The scheme avoids completely
spectral decomposition into characteristic waves, computationally expensive and
subject to many degenerate cases in the magnetic case, while it makes use of a
two-speed Riemann solver that just require the knowledge of the two local fast
magnetosonic velocities. Moreover, the onset of spurious magnetic monopoles,
which is a typical problem for multi-dimensional MHD upwind codes, is prevented
by properly taking into account the solenoidal constraint and the specific
antisymmetric nature of the induction equation. Finally, the extension to
generalized orthogonal curvilinear coordinate systems is included, thus the
scheme is ready to incorporate general relativistic (GRMHD) effects.
