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We propose a new formulation of chiral fermions on a lattice, on the basis ofa lattice extension of the covariant regularization scheme in continuum fieldtheory. The species doublers do not emerge. The real part of the effectiveaction is just one half of that of Dirac-Wilson fermion and is always gaugeinvariant even with a finite lattice spacing. The gauge invariance of theimaginary part, on the other hand, sets a severe constraint which is a latticeanalogue of the gauge anomaly free condition. For real gauge representations,the imaginary part identically vanishes and the gauge invariance becomes exact.Comment: 15 pages, PHYZZX. The title is changed. The final version to appear  in Phys. Rev.

Manifestly gauge covariant treatment of lattice chiral fermions. II