  We discuss a specific cut-off effect which appears in applying the
non-perturbative RI/MOM scheme to compute the renormalization constants. To
illustrate the problem a Dirac operator satisfying the Ginsparg-Wilson relation
is used, but the arguments are more general. We propose a simple modification
of the method which gets rid of the corresponding discretization error.
Applying this to full-QCD simulations done at a=0.13 fm with the Fixed Point
action we find that the renormalization constants are strongly distorted by the
artefacts discussed. We consider also the role of global gauge transformations,
a freedom which still remains after the conventional gauge fixing procedure is
applied.
