  Iterating renormalization group transformations for lattice fermions the
Wilson action is driven to fixed points of the renormalization group. A line of
fixed points is found and the fixed point actions are computed analytically.
They are local and may be used to improve scaling in lattice QCD. The action at
the line's endpoint is chirally invariant and still has no fermion doubling.
The Nielsen-Ninomiya theorem is evaded because in this case the fixed point
action is nonlocal. The use of this action for a construction of lattice chiral
fermions is discussed.
