  We analyze the main geometric conditions imposed by the hypothesis of the
Jebsen-Birkhoff theorem. We show that the result (existence of an additional
Killing vector) does not necessarily require a three-dimensional isometry group
on two-dimensional orbits but only the existence of a conformal Killing-Yano
tensor. In this approach the (additional) isometry appears as the known
invariant Killing vector that the ${\cal D}$-metrics admit.
