  In this paper we introduce a new class of theories which dynamically break
supersymmetry based on the gauge group SU(n)xSU(3)xU(1) for even n. These
theories are interesting in that no dynamical superpotential is generated in
the absence of perturbations. For the example SU(4)xSU(3)xU(1) we explicitly
demonstrate that all flat directions can be lifted through a renormalizable
superpotential and that supersymmetry is dynamically broken. We derive the
exact superpotential for this theory, which exhibits new and interesting
dynamical phenomena. For example, modifications to classical constraints can be
field dependent. We also consider the generalization to SU(n)xSU(3)xU(1) models
(with even n>4). We present a renormalizable superpotential which lifts all
flat directions. Because SU(3) is not confining in the absence of
perturbations, the analysis of supersymmetry breaking is very different in
these theories from the n=4 example. When the SU(n) gauge group confines, the
Yukawa couplings drive the SU(3) theory into a regime with a dynamically
generated superpotential. By considering a simplified version of these theories
we argue that supersymmetry is probably broken.
