We recalculate the beta functions of higher-derivative gravity in four dimensions using the one-loop approximation to an exact renormalization group equation. We reproduce the beta functions of the dimensionless couplings that were known in the literature, but we find new terms for the beta functions of Newton's constant and of the cosmological constant. As a result, the theory appears to be asymptotically safe at a non-Gaussian fixed point rather than perturbatively renormalizable and asymptotically free.