Non-perturbative running of the coupling from four flavour lattice QCD with staggered quarks

Using the Schr\"odinger functional (SF) with a single staggered fermion field we calculate the SF coupling in four-flavour QCD for a wide range of energies and lattice sizes up to $L/a=16$. Preliminary results for the continuum extrapolation of the step-scaling function are presented. To reduce cutoff effects, one-loop ${\rm O}(a)$ improvement has been implemented. Various cross checks are made possible by the use of two independent sets of lattices with either $T=L+a$ or $T=L-a$.