  We consider the Markov random flight $\bold X(t), \; t>0,$ in the
three-dimensional Euclidean space $\Bbb R^3$ with constant finite speed $c>0$
and the uniform choice of the initial and each new direction at random time
instants that form a homogeneous Poisson flow of rate $\lambda>0$. Series
representations for the conditional characteristic functions of $\bold X(t)$
corresponding to two and three changes of direction, are obtained. Based on
these results, an asymptotic formula, as $t\to 0$, for the unconditional
characteristic function of $\bold X(t)$ is derived. By inverting it, we obtain
an asymptotic relation for the transition density of the process. We show that
the error in this formula has the order $o(t^3)$ and, therefore, it gives a
good approximation on small time intervals whose lengths depend on $\lambda$.
Estimate of the accuracy of the approximation is analysed.
