  In order to obtain a well-defined path integral one often employs
discretizations. In the case of General Relativity these generically break
diffeomorphism symmetry, which has severe consequences since these symmetries
determine the dynamics of the corresponding system.
  In this article we consider the path integral of reparametrization invariant
systems as a toy example and present an improvement procedure for the
discretized propagator. Fixed points and convergence of the procedure are
discussed. Furthermore we show that a reparametrization invariant path integral
implies discretization independence and acts as a projector onto physical
states.
