  Properties of amplitudes that describe radiative corrections in a bag of
heavy fermions bound by the Higgs boson exchange are studied. Classes of
amplitudes, in which the large fermion mass is canceled out and hence produces
no enhancement for the radiative corrections are found. For fermions with
masses in the region 400< m < 1000 Gev all relevant amplitudes are found to
possess this property. Correspondingly the radiative corrections for this range
of masses are small. For very heavy fermions, m>1000 Gev, the processes
described by diagrams with closed fermion loops are also mass-independent.
