  We show that the representation of black-hole solutions in terms of the
variables H^M which are harmonic functions in the supersymmetric case is
non-unique due to the existence of a local symmetry in the effective action.
This symmetry is a continuous (and local) generalization of the discrete
Freudenthal transformations initially introduced for the black-hole charges and
can be used to rewrite the physical fields of a solution in terms of entirely
different-looking functions.
