  We compute, neglecting possible effects of subleading irrelevant couplings,
the localization length exponent in the integer quantum Hall effect, for the
case of white noise random potentials. The result obtained is $\nu=2$ for all
Landau levels. Our approach consists in a renormalization group transformation
of Landau orbitals, which iterates the generating functional of Green's
functions for the localization problem. The value of $\nu$ is obtained from the
asymptotic form of the renormalization group mapping. The basic assumptions in
our derivation are the existence of a scaling law for the localization length
and the absence of Landau level mixing.
