  A five dimensional pure Yang--Mills theory, with the fifth coordinate
compactified on the orbifold $S^1/Z_2$ of radius R, leads to a four dimensional
theory which is governed by two types of local gauge transformations, namely,
the well known standard gauge transformations (SGT) dictated by the $SU_4(N)$
group under which the zero Fourier modes transform as gauge fields, and a set
of nonstandard gauge transformations (NSGT) determining the gauge nature of the
Kaluza--Klein (KK) excitations. By using a SGT-covariant gauge-fixing procedure
for removing the degeneration associated with the NSGT, we integrate out the KK
excitations and obtain a low-energy effective Lagrangian expansion involving
all of the independent canonical-dimension-six operators that are invariant
under the SGT of the $SU_4(N)$ group and that are constituted by light gauge
fields (zero modes), exclusively. It is shown that this effective Lagrangian is
invariant under the SGT, but it depends on the gauge-fixing of the gauge KK
excitations. Our result shows explicitly that the one-loop contributions of the
KK excitations to light (standard) Green's functions are renormalizable.
