  In string theory it is known that abelian isometries in the sigma model lead
to target space duality. We generalize this duality to backgrounds with
non--abelian isometries. The procedure we follow consists of gauging the
isometries of the original action and constraining the field strength $F$ to
vanish. This new action generates dual theories by integrating over either the
Lagrange multipliers that set F=0 or the gauge fields. We find that this new
duality transformation maps spaces with non--abelian isometries to spaces that
may have no isometries at all. This suggests that duality symmetries in string
theories need to be understood in a more general context without regard to the
existence of continuous isometries on the target space (this is also indicated
by the existence of duality in string compactifications on Calabi--Yau
manifolds which have no continuous isometries). Physically interesting examples
to which our formalism apply are the Schwarzschild metric and the 4D charged
dilatonic black hole. For these spherically symmetric black holes in four
dimensions, the dual backgrounds are presented and explicitly shown to be new
solutions of the leading order string equations. Some of these new backgrounds
are found to have no continuous isometries (except for time translations) and
also have naked singularities.
