Let
$g:\,{{M}^{2n}}\,\to \,{{M}^{2n}}$
be a smooth map of period
$m\,>\,2$
which preserves orientation. Suppose that the cyclic action defined by
$g$
is regular and that the normal bundle of the fixed point set
$F$
has a
$g$
-equivariant complex structure. Let
$F\,\pitchfork \,F$
be the transverse self-intersection of
$F$
with itself. If the
$g$
-signature
$\text{Sign(g,}\,\text{M)}$
is a rational integer and
$n\,<\,\phi (m)$
, then there exists a choice of orientations such that
$\text{Sign}\,\text{(g,}\,\text{M)}\,\text{=}\,\text{Sign}\,\text{F}\,\text{=}\,\text{Sign}(F\,\pitchfork \,F)$
.