  In non-commutative field theories conventional wisdom is that the unitarity
is non-compatible with the perturbation analysis when time is involved in the
non-commutative coordinates. However, as suggested by Bahns et.al. recently,
the root of the problem lies in the improper definition of the time-ordered
product. In this article, functional formalism of S-matrix is explicitly
constructed for the non-commutative $\phi^p$ scalar field theory using the
field equation in the Heisenberg picture and proper definition of
time-ordering. This S-matrix is manifestly unitary. Using the free spectral
(Wightmann) function as the free field propagator, we demonstrate the
perturbation obeys the unitarity, and present the exact two particle scattering
amplitude for 1+1 dimensional non-commutative nonlinear Schr\"odinger model.
