  The scaling of the Schr"odinger functional coupling is studied numerically
and perturbatively for an SU(3) lattice gauge field coupled to an O(a) improved
bosonic spinor field. This corresponds to QCD with minus two light flavours and
is used as a numerically less costly test case for real QCD. A suitable
algorithm is developed, and the influence of the matter fields on the continuum
limit and the lattice artefacts are studied in detail.
