  The Yang-Mills gradient flow in finite volume is used to define a running
coupling scheme. As our main result the discrete beta-function, or step scaling
function, is calculated for scale change s=3/2 at several lattice spacings for
SU(3) gauge theory coupled to N_f = 4 fundamental massless fermions. The
continuum extrapolation is performed and agreement is found with the continuum
perturbative results for small renormalized coupling. The case of SU(2) gauge
group is briefly commented on.
