  The relativistic generalization of a free Brownian motion theory is
presented. The global characteristics of the relaxation are {\it explicitly}
found for the velocity and momentum (stochastic) kinetics. It is shown that the
thermal corrections, to the both relaxation times $T$ (of stationary
autocorrelations) and transient relaxation time of momentum, appear slowing
down the processes. The transient relaxation time of the velocity does not
depend {\it explicitly} on temperature, $T(v_0)= m(v_0)/\gamma \equiv
\epsilon_0/\gamma c^2$, and it is proportional to the initial energy of a
relativistic Brownian particle.
