  In the paper we consider the Stiefel manifold $V_{n;k}$ as a principal
$U(k)$- bundle over the Grassmann manifold and study the cut locus from the
unit element. We gave the complete description of this cut locus on $V_{n;1}$
and presented the sufficient condition on the general case. At the end, we
study the complement to the cut locus of $V_{2k;k}$.
