  In this article we calculate several divergent amplitudes in phi^4-theory on
non-commutative space-time in the framework of Interaction Point Time Ordered
Perturbation Theory (IPTOPT), continuing work done in hep-th/0209253. On the
ground of these results we find corresponding Feynman rules which allow for a
much easier diagrammatic calculation of amplitudes. The most important feature
of the present theory is the lack of the UV/IR mixing problem in all amplitudes
calculated so far. Although we are not yet able to give a rigorous proof, we
provide a strong argument for this result to hold in general. Together with the
found Feynman rules this opens promising vistas towards the systematic
renormalization of non-commutative field theories.
