  We study the non-perturbative renormalization group flow of higher-derivative
gravity employing functional renormalization group techniques. The
non-perturbative contributions to the $\beta$-functions shift the known
perturbative ultraviolet fixed point into a non-trivial fixed point with three
UV-attractive and one UV-repulsive eigendirections, consistent with the
asymptotic safety conjecture of gravity. The implication of this transition on
the unitarity problem, typically haunting higher-derivative gravity theories,
is discussed.
