  The beta function of the multichannel Kondo model is calculated exactly in
the limit of large spin N and channel number M=gamma*N, with constant gamma.
There are no corrections in any finite order of 1/N. One zero is found at a
finite coupling strength, showing directly the Non--Fermi liquid behavior of
the model. This renormalization group flow allows to introduce a variational
principle for the entropy, to obtain the low temperature thermodynamics. Such
in particular the low temperature thermodynamics of the non--crossing
approximation to the Kondo model becomes accessible.
