  We show that a lattice model for induced lattice QCD which was recently
proposed by Kazakov and Migdal has a $Z_N$ gauge symmetry which, in the strong
coupling phase, results in a local confinement where only color singlets are
allowed to propagate along links and all Wilson loops for non-singlets average
to zero. We argue that, if this model is to give QCD in its continuum limit, it
must have a phase transition. We give arguments to support presence of such a
phase transition.
