  The kinematics of a particle with the upper bound on the particle's speed (a
modification of classical kinematics where such a restriction is absent) has
been developed in [arXiv:1204.5740]. It was based solely on classical mechanics
without employing any concepts , associated with the time dilatation or/and
length contraction. It yielded the 1-D Lorentz transformation (LT), free of
inconsistencies (inherent in the canonical derivation and interpretations of
the LT). Here we apply the same approach to derive the LT for the 3-dimensional
motion of a particle and the attendant law of velocity composition. As a
result, the infinite set of four-parameter transformations is obtained. The
requirement of linearity of these transformations selects out of this set the
two-parameter subset . The values of the remaining two parameters ,dictated by
physics of the motion, is explicitly determined , yielding the canonical form
of the 3-dimensional LT. The generalized law of velocity composition and the
attendant invariant ( not postulated apriori) of the motion are derived, As in
the one-dimensional case, present derivation, as a whole, does not have any
need in introducing the concepts of the time dilatation and length contraction,
and is based on the classical concepts of time and space.
