We describe an algorithm that computes the linear dispersion relation of waves and instabilities in relativistic plasmas within a Vlasov–Maxwell description. The method used is fully relativistic and involves explicit integration of particle orbits along the unperturbed equilibrium trajectories. We check the algorithm against the dispersion curves for a single component magnetized plasma and for an unmagnetized plasma with counter-streaming components in the nonrelativistic case. New results on the growth rate of the Weibel or two-stream instability in a hot unmagnetized pair plasma consisting of two counter-streaming relativistic Maxwellians are presented. These are relevant to the physics of the relativistic plasmas found in gamma-ray bursts, relativistic jets and pulsar winds.