  In this paper, by performing a general Kaluza-Klein (KK) decomposition, we
obtain a gauge invariant effective action for a bulk massless $q$-form field on
a $p$-brane with codimension two. There appear four types of KK modes: two
$(q-1)$-forms and one $(q-2)$-form in addtion to the ordinary $q$-form, which
are essential for the gauge invariance. Due to the two extra dimensions, we
find eight Schr\"{o}dinger-like equations for the four modes and their mass
spectra are closely related. Moreover, via this decomposition mechanism, the
Hodge duality in the bulk naturally induces four coupled dualities on the
brane, which guarantees that the physical equavalence of bulk dual fields is
preserved under the dimensional reduction.
