We consider the gravitational coupling of a scalar field, in a reformu
lation of General Relativity exhibiting local GL(4) invariance at the
classical level. We compute the one-loop contribution of the scalar to
the quantum effective potential of the vierbein and find that it does
not have GL(4) invariance. The minima of the effective potential occu
r for a vierbein which is proportional to the unit matrix.