In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.