Let be a germ of a holomorphic self-map of at the origin tangent to the identity, and with as a nondicritical isolated fixed point. A parabolic curve for is a holomorphic -invariant curve, with on the boundary, attracted by under the action of . It has been shown by M. Abate (2001) that if the characteristic direction has residual index not belonging to , then there exist parabolic curves for tangent to . In this paper we prove, using a different method, that the conclusion still holds just assuming that the residual index is not vanishing (at least when is regular along ).