  We compute the two-point and four-point Green's function of the
noncommutative $\phi^{4}$ field theory; first with the s-ordered star products
and then with a general translation invariant star product. We derive the
differential expression for any translation invariant star product, and with
the help of this expression we show that any of these products can be written
in terms of a twist. Finally, using the notion of the twisted action of the
infinitesimal Poincar\'e transformations, we show that the commutator between
the coordinate functions is invariant under Poincar\'e transformations at a
deformed level.
