  Asymptotic normalization coefficients (ANCs) are fundamental nuclear
constants playing important role in nuclear reactions, nuclear structure and
nuclear astrophysics. In this paper the physical reasons of the Coulomb
renormalization of the ANC are addressed. Using Pinkston-Satchler equation the
ratio for the proton and neutron ANCs of mirror nuclei is obtained in terms of
the Wronskians from the radial overlap functions and regular solutions of the
two-body Schr\"odinger equation with the short-range interaction excluded. This
ratio allows one to use microscopic overlap functions for mirror nuclei in the
internal region, where they are the most accurate, to correctly predict the
ratio of the ANCs for mirror nuclei, which determine the amplitudes of the
tails of the overlap functions. Calculations presented for different nuclei
demonstrate the Coulomb renormalization effects and independence of the ratio
of the nucleon ANCs for mirror nuclei on the channel radius. This ratio is
valid both for bound states and resonances. One of the goals of this paper is
to draw attention on the possibility to use the Coulomb renormalized ANCs
rather than the standard ones especially when the standard ANCs are too large.
