  We calculate the low-energy constant $L_{10}$ in a two-representation SU(4)
lattice gauge theory that is close to a composite-Higgs model. From this we
obtain the contribution of the new strong sector to the $S$ parameter. This
leads to an upper bound on the vacuum misalignment parameter $\xi$ which is
similar to current estimates of this bound. Our result agrees with large-$N_c$
scaling expectations, within large systematic uncertainties.
