  We consider the asymptotic-safety scenario for quantum gravity which
constructs a non-perturbatively renormalisable quantum gravity theory with the
help of the functional renormalisation group. We verify the existence of a
non-Gaussian fixed point and include a running curvature-ghost coupling as a
first step towards the flow of the ghost sector of the theory. We find that the
scalar curvature-ghost coupling is asymptotically free and RG relevant in the
ultraviolet. Most importantly, the property of asymptotic safety discovered so
far within the Einstein-Hilbert truncation and beyond remains stable under the
inclusion of the ghost flow.
