  We prove that for arbitrary black brane solutions of generic Supergravities
there is an adapted system of variables in which the equations of motion are
exactly invariant under electric-magnetic duality, i.e. the interchange of a
given extended object by its electromagnetic dual. We obtain thus a procedure
to automatically construct the electromagnetic dual of a given brane without
needing to solve any further equation. We apply this procedure to construct the
non-extremal (p, q)-string of Type-IIB String Theory (new in the literature),
explicitly showing how the dual (p, q)-five-brane automatically arises in this
construction. In addition, we prove that the system of variables used is
suitable for a generic characterization of every double-extremal Supergravity
brane solution, which we perform in full generality.
