  We generalize the supersymmetry method in Random Matrix Theory to arbitrary
rotation invariant ensembles. Our exact approach further extends a previous
contribution in which we constructed a supersymmetric representation for the
class of norm-dependent Random Matrix Ensembles. Here, we derive a
supersymmetric formulation under very general circumstances. A projector is
identified that provides the mapping of the probability density from ordinary
to superspace. Furthermore, it is demonstrated that setting up the theory in
Fourier superspace has considerable advantages. General and exact expressions
for the correlation functions are given. We also show how the use of hyperbolic
symmetry can be circumvented in the present context in which the non-linear
sigma model is not used. We construct exact supersymmetric integral
representations of the correlation functions for arbitrary positions of the
imaginary increments in the Green functions.
