  In this paper, imposing hermitian conjugate relations on the two-parameter
deformed quantum group GL_{p,q}(2) is studied. This results in a
non-commutative phase associated with the unitarization of the quantum group.
After the achievement of the quantum group U_{p,q}(2) with pq real via a
non-commutative phase, the representation of the algebra is built by means of
the action of the operators constituting the U_{p,q}(2) matrix on states.
