  It is shown that within conformally flat stationary axisymmetric spacetimes,
besides of the static family, there exists a new class of metrics, which is
always stationary and axisymmetric. All these spacetimes, the static and the
stationary ones, are endowed with an arbitrary function depending on the two
non--Killingian coordinates. The explicit form of this function can be
determined once the coupled matter, i.e., the energy--momentum tensor is given.
One might hope possible extensions of this result to black holes on two--branes
in four dimensions.
