  We present a scaling investigation of some correlation functions in $\Or(a)$
improved quenched lattice QCD. In particular, as one observable the
renormalized PCAC quark mass is considered. Others are constructed such that
they become the vector meson mass and the pseudoscalar meson decay constant
when the volume is large. For the present discussion we remain in intermediate
volume, $(0.75^3\times1.5) {fm}^4$ with Schr\"odinger functional boundary
conditions. By fixing the `pion mass' and the spatial lattice size in units of
the hadronic scale $r_0$, we simulated four lattices with resolutions ranging
from 0.1 fm to 0.05 fm and performed the extrapolation to the continuum limit.
The maximal scaling violation found in the improved theory is a $\sim$ 6 %
effect at $a\simeq 0.1 fm$.
