  We analyze intersecting brane models on toroidal orbifolds T^4/Z_N(N=3,4,6).
Focusing on several Higgsing processes of intersecting brane models, we have
some insights into the matter spectrum on intersecting branes away from
orientifold planes. The matter fields in the adjoint representations of the
gauge group on branes can arise when brane intersects the orientifold images.
Gauge group and matter spectrum are confirmed using Chan-Paton methods with the
Higgsing processes.
