  We present evidence for the universality of the continuum limit of the scale
dependence of the renormalization constant associated with the operator
corresponding to the average momentum of non-singlet parton densities. The
evidence is provided by a non-perturbative computation in quenched lattice QCD
using the Schr\"odinger Functional scheme. In particular, we show that the
continuum limit is independent of the form of the fermion action used, i.e. the
Wilson action and the non-perturbatively improved clover action.
