We consider a modification of the Wilson-Yukawa model to overcome the difficulty that the fermion mass is not proportional to the Higgs vacuum expectation value. In the modification scalar and fermionic regular fields are introduced so that all the physical fermion fields possess shift symmetry when the Yukawa coupling vanishes. With the fermionic hopping parameter expansion it is shown that the fermion mass is proportional to the Higgs vacuum expectation value. We find, however, that the coupling of fermion to the external gauge field is always vectorlike in the continuum limit and that further modifications to the scalar action cannot change this undesirable conclusion.