  We consider the Hamiltonian BRST quantization of a noncommutative non abelian
gauge theory. The Seiberg-Witten map of all phase-space variables, including
multipliers, ghosts and their momenta, is given in first order in the
noncommutative parameter $\theta$. We show that there exists a complete
consistence between the gauge structures of the original and of the mapped
theories, derived in a canonical way, once we appropriately choose the map
solutions.
