  An exploratory numerical study of the influence of heavy fermion doublets on
the mass of the Higgs boson is performed in the decoupling limit of a chiral
$\rm SU(2)_L \otimes SU(2)_R$ symmetric Yukawa model with mirror fermions. The
behaviour of fermion and boson masses is investigated at infinite bare quartic
coupling on $4^3 \cdot 8$, $6^3 \cdot 12$ and $8^3 \cdot 16$ lattices. A first
estimate of the upper bound on the renormalized quartic coupling as a function
of the renormalized Yukawa-coupling is given.
