We investigate the role of the Gauss-Bonnet term for the n = 4 and n = 4-e renormalization group, for both conformal and general versions of the theory. The cancellation of the quantum effects of the Gauss-Bonnet term in the n = 4 limit represents an efficient test for the correctness of previous calculations and also resolves two long-standing problems concerning quantum corrections in quantum gravity. In the case of n = 4-epsilon renormalization group there is a number of new nontrivial fixed points, that may indicate to a rich nonperturbative structure of the theory. At the same time, if we do not treat e as a small parameter, the renormalization group is spoiled by an extensive gauge fixing ambiguity.