  The large N effective action of the non-linear sigma model based in the coset
O(N+1)/O(N) is obtained. The renormalization of this effective action requires
the introduction of an infinite set of counterterms. However, there exit
particular cases where, at some scale, only a finite number of non-zero
coupling constants are present. This fact makes possible a one parameter fit of
the I=J=0 low-energy pion scattering. The corresponding non-local effective
action is used to study the properties of the skyrmion which is shown to be
unstable in this approximation.
