  The left and right handed fermion zero-modes are examined. Their behaviour
under the variation of the size of the instanton, $\ri$, and the size of the
Higgs core, $\rh$, for a range of Yukawa couplings corresponding to the fermion
masses in the electroweak theory are studied. It is shown that the
characteristic radii of the zero-modes, in particlar those the left handed
fermions, are locked to the instanton size, and are not affected by the
variation of $\rh$, except for fermion masses much larger than those in the
standard electroweak theory.
