We consider the random motion of a particle that moves with constant finite speed in the space ℝ
4 and, at Poisson-distributed times, changes its direction with uniform law on the unit four-sphere. For the particle's position,
X
(t) = (X
1(t), X
2(t), X
3(t), X
4(t)), t > 0, we obtain the explicit forms of the conditional characteristic functions and conditional distributions when the number of changes of directions is fixed. From this we derive the explicit probability law, f(
x
, t), x ∈ ℝ
4, t ≥ 0, of
X
(t). We also show that, under the Kac condition on the speed of the motion and the intensity of the switching Poisson process, the density, p(
x
,t), of the absolutely continuous component of f(
x
,t) tends to the transition density of the four-dimensional Brownian motion with zero drift and infinitesimal variance σ2 = ½.