  We introduce a non-perturbative improvement for the renormalization group
step scaling function based on the gradient flow running coupling, which may be
applied to any lattice gauge theory of interest. Considering first SU(3) gauge
theory with $N_f = 4$ massless staggered fermions, we demonstrate that this
improvement can remove $O(a^2)$ lattice artifacts, and thereby increases our
control over the continuum extrapolation. Turning to the 12-flavor system, we
observe an infrared fixed point in the infinite-volume continuum limit.
Applying our proposed improvement reinforces this conclusion by removing all
observable $O(a^2)$ effects. For the finite-volume gradient flow
renormalization scheme defined by $c = \sqrt{8t} / L = 0.2$, we find the
continuum conformal fixed point to be located at $g_\star^2 = 6.2(2)$
