  We find the probability density function $\mathcal{P}(V_{\texttt{r}})$ of the
relativistic relative velocity for two colliding particles in a non-degenerate
relativistic gas. The distribution reduces to Maxwell distribution for the
relative velocity in the non-relativistic limit. We find an exact formula for
the mean value $\langle V_{\texttt{r}}\rangle$. The mean velocity tends to the
Maxwell's value in the non-relativistic limit and to the velocity of light in
the ultra-relativistic limit. At a given temperature $T$, when at least for one
of the two particles the ratio of the rest energy over the thermal energy $m
c^2/k_B T$ is smaller than 40 the Maxwell distribution is inadequate.
