  We examine Podolsky's electrodynamics, which is noninvariant under the usual
duality transformation. We deduce a generalization of Hodge's star duality,
which leads to a dual gauge field and restores to a certain extent the dual
symmetry. The model becomes fully dual symmetric asymptotically when it reduces
to the Maxwell theory. We argue that this strict dual symmetry directly implies
the existence of the basic invariants of the electromagnetic fields.
