We study the effect of meson loops on the chiral anomaly action given by Witten as an integral over a five dimensional space. The coefficient of the anomaly, quantized in terms of the number of colors, is not modified by loops. All of the loop corrections are given by local four-dimensional chiral Lagrangians which contribute, in higher order in the momenta, to the same physical processes as the anomaly. We discuss the modifications of the decays π0 → γγ, η → γγ, π0 → γℓ+ℓ−, η → γℓ+ℓ−.