Recently, Gliozzi has shown that, under certain conditions, it is possible to derive the Dirac-Born-Infeld action for an Abelian gauge field of a D-brane. Also, the action turns out to be invariant with respect to a nonlinear realization of the full Poincaré group. A crucial role is played by the transformation properties of the gauge field under the nonlinear realization. The aim of this paper is to point out that these transformation properties are derived directly from the gauge fixing of the diffeomorphisms of the brane and the necessary compensating reparametrization when one performs a Lorentz transformation.