  We construct a 4-d lattice Dirac operator D using a systematical expansion in
terms of simple operators on the lattice. The Ginsparg-Wilson equation turns
into a system of coupled equations for the expansion coefficients of D. We
solve these equations for a finite parametrization of D and find an approximate
solution of the Ginsparg-Wilson equation. We analyze the spectral properties of
our D for various ensembles of quenched SU(3) configurations. Improving the
gauge field action considerably improves the spectral properties of our D.
