  We re-examine the approach to four-dimensional Euclidean quantum gravity
based on the Regge calculus. A cut-off on the link lengths is introduced and
consequently the gravitational coupling and the cosmological constant become
independent parameters. We determine the zero curvature, $<R> =0$, line in the
coupling constant plane by numerical simulations. When crossing this line we
find a strong, probably first order, phase transition line with indications of
a second order endpoint. Beyond the endpoint the transition through the $<R>
=0$ line appears to be a crossover. Previous investigations, using the Regge or
the Dynamical Triangulation approach, dealt with a limit in which the first
order transition prevails.
