  In this paper, the BRST symmetry transformation is presented for the
noncommutative U(N) gauge theory. The nilpotency of the charge associated to
this symmetry is then proved. As a consequence for the space-like
non-commutativity parameter, the Hilbert space of physical states is determined
by the cohomology space of the BRST operator as in the commutative case.
Further, the unitarity of the S-matrix elements projected onto the subspace of
physical states is deduced.
