  The free energy and magnetization for the general $SU(N)$ one impurity Kondo
model in the magnetic field, $h$, are calculated by extending the previous
$1/N$ expansion technique: the saddle point is determined self-consistently to
the $1/N$ order. The obtained universal field dependent magnetization
$M(h/T_{K})$ by this simple method is shown analytically to be asymptotically
exact at both $h \ll T_{K}$ and $h \gg T_{K}$ limits. For general
''$f$-electron'' fillings, except half filling, the $M(h/T_{K})$ curves cross
continuously from weak to strong coupling limit, but overestimate the curvature
in the crossover region for moderate $N$.
  The magnetic Wilson crossover numbers are calculated for amusement. Our
results explicitly verify that the $1/N$ parameter is non-singular under the
adiabatic continuation.
