  We show the consistent interactions in the generalized electrodynamics gauge
theory with higher derivative matter fields by means of the order reduction
method. We deduce the BRST deformations in the reduced Lagrangian and using the
equations of motion of the auxiliary fields in the antighost number zero part
in the resulting deformed action, we are able to obtain the consistent coupling
terms added into the original Lagrangian density which are compatible with the
deformation master equations. We emphasize that the order of deformations is
truncated at four and the corresponding higher-order deformations are equal to
zero precisely. Moreover, the local Abelian gauge symmetry turns out to be
non-Abelian after the deformation procedure.
