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

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