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.