  The integrability conditions for the existence of a conformal Killing-Yano
tensor of arbitrary order are worked out in all dimensions and expressed in
terms of the Weyl tensor. As a consequence, the integrability conditions for
the existence of a Killing-Yano tensor are also obtained. By means of such
conditions, it is shown that in certain Einstein spaces one can use a conformal
Killing-Yano tensor of order p to generate a Killing-Yano tensor of order
(p-1). Finally, it is proved that in maximally symmetric spaces the covariant
derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor
and that every conformal Killing-Yano tensor is uniquely decomposed as the sum
of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.
