  We compute the beta functions of Higher Derivative Gravity within the
Functional Renormalization Group approach, going beyond previously studied
approximations. We find that the presence of a nontrivial Newtonian coupling
induces, in addition to the free fixed point of the one-loop approximation,
also two nontrivial fixed points, of which one has the right signs to be free
from tachyons. Our results are consistent with earlier suggestions that the
dimension of the critical surface for pure gravity is three.
