  A Ginsparg-Wilson Relation (GWR) is obtained in the presence of chiral
symmetry breaking terms. It leads to the PCAC relation as well as an anomaly
relation on the lattice. For general fermions, the deviation from the exact GWR
is getting small when the block-spin transformations are performed iteratively.
Based on a simple geometrical interpretation of the Dirac operator satisfying
the GWR, we find some physical properties shared by the lattice fermions near
the continuum limit. In two-dimensions, we explicitly construct the GW Dirac
operator by using a conformal mapping.
