  A Riemann problem with prescribed initial conditions will produce one of
three possible wave patterns corresponding to the propagation of the different
discontinuities that will be produced once the system is allowed to relax. In
general, when solving the Riemann problem numerically, the determination of the
specific wave pattern produced is obtained through some initial guess which can
be successively discarded or improved. We here discuss a new procedure,
suitable for implementation in an exact Riemann solver in one dimension, which
removes the initial ambiguity in the wave pattern. In particular we focus our
attention on the relativistic velocity jump between the two initial states and
use this to determine, through some analytic conditions, the wave pattern
produced by the decay of the initial discontinuity. The exact Riemann problem
is then solved by means of calculating the root of a nonlinear equation.
Interestingly, in the case of two rarefaction waves, this root can even be
found analytically. Our procedure is straightforward to implement numerically
and improves the efficiency of numerical codes based on exact Riemann solvers.
