  Noncommutative quantum field theory of a complex scalar field is considered.
There is a two-coupling noncommutative analogue of U(1)-invariant quartic
interaction $(\phi^*\phi)^2$, namely $A\phi^*\star\phi\star\phi^*\star\phi+
B\phi^*\star\phi^*\star\phi\star\phi$. For arbitrary values of $A$ and $B$ the
model is nonrenormalizable. However, it is one-loop renormalizable in two
special cases: B=0 and $A=B$. Furthermore, in the case B=0 the model does not
suffer from IR divergencies at least at one-loop insertions level.
