  Let f be a germ of holomorphic self-map of C^2 at the origin O tangent to the
identity, and with O as a non-dicritical isolated fixed point. A parabolic
curve for f is a holomorphic f-invariant curve, with O on the boundary,
attracted by O under the action of f. It has been shown that if the
characteristic direction [v] has residual index not belonging to Q^+, then
there exist parabolic curves for f tangent to [v]. In this paper we prove, with
a different method, that the conclusion still holds just assuming that the
residual index is not vanishing (at least when f is regular along [v]).

Complex Variables