Let f : U →R2 be a continuous map, where U is an open
subset of R2. We consider a fixed point p of f which is neither a sink nor
a source and such that p is an isolated invariant set. Under these assumption
we prove, using Conley index methods and Nielsen theory, that the sequence of fixed point indices of iterations ind(fn, p) n=1 is periodic,bounded by 1, and has infinitely many non-positive terms, which is a generalization of Le Calvez and Yoccoz theorem [Annals of Math., 146 (1997), 241-293] onto the class of non-injective maps.