  The nonstandard q-deformation $U'_q({\rm so}_n)$ of the universal enveloping
algebra $U({\rm so}_n)$ has irreducible finite dimensional representations
which are a q-deformation of the well-known irreducible finite dimensional
representations of $U({\rm so}_n)$. But $U'_q({\rm so}_n)$ also has irreducible
finite dimensional representations which have no classical analogue. The aim of
this paper is to give these representations which are called nonclassical type
representations. They are given by explicit formulas for operators of the
representations corresponding to the generators of $U'_q({\rm so}_n)$.
