  A necessary condition that a St\"ackel-Killing tensor of valence 2 be the
contracted product of a Killing-Yano tensor of valence 2 with itself is
re-derived for a Riemannian manifold. This condition is applied to the
generalized Euclidean Taub-NUT metrics which admit a Kepler type symmetry. It
is shown that in general the St\"ackel-Killing tensors involved in the
Runge-Lenz vector cannot be expressed as a product of Killing-Yano tensors. The
only exception is the original Taub-NUT metric.
