Generalized Taub-NUT metrics and Killing-Yano tensors

The necessary condition that a Stackel-Killing tensor of valence two should be the contracted product of a Killing-Yano tensor of valence two with itself is rederived 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 Stacker-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.