  The ${\rm SU}(2)$-prolongation of the Hopf fibration $S^3\to S^2$ is a
trivializable principal ${\rm SU}(2)$-bundle. We present a noncommutative
deformation of this bundle to a quantum principal ${\rm SU}_q(2)$-bundle that
is not trivializable. On the other hand, we show that the ${\rm
SU}_q(2)$-bundle is piecewise trivializable with respect to the closed covering
of $S^2$ by two hemispheres intersecting at the equator.
