  The behaviour of the master field in ``induced QCD" near the edge of its
support is studied. An extended scaling domain, where the shape of the master
field is a universal function, is found. This function is determined explicitly
for the case of dimensions, close to one, and the $D-1$-expansion is
constructed. The problem of the meson spectrum corresponding to this solution
is analyzed. As a byproduct of these calculations, a new, explicit equation for
the meson spectrum in ``induced QCD" with a general potential is derived.
