  We propose two new realizations of the N=4, $\hat{c}=4$ superconformal system
based on the compact and non-compact versions of parafermionic algebras. The
target space interpretation of these systems is given in terms of
four-dimensional target spaces with non-trivial metric and topology different
from the previously known four-dimensional semi-wormhole realization. The
proposed $\hat{c}=4$ systems can be used as a building block to construct
perturbatively stable superstring solutions with covariantized target space
supersymmetry around non-trivial gravitational and dilaton backgrounds.
