  We non-perturbatively determine the renormalization constant and the
improvement coefficients relating the renormalized current and subtracted quark
mass in O(a) improved two-flavour lattice QCD. We employ the Schr\"odinger
functional scheme and fix the physical extent of the box by working at a
constant value of the renormalized coupling. Our calculation yields results
which cover two regions of bare parameter space. One is the weak-coupling
region suitable for volumes of about half a fermi. By making simulations in
this region, quarks as heavy as the bottom can be propagated with the full
relativistic QCD action and renormalization problems in HQET can be solved
non-perturbatively by a matching to QCD in finite volume. The other region
refers to the common parameter range in large-volume simulations of two-flavour
lattice QCD, where our results have particular relevance for charm physics
applications.
