  We present results for the renormalized quartic self-coupling $\lambda_R$ and
the Yukawa coupling $y_R$ in a lattice fermion-Higgs model with two SU(2)$_L$
doublets, mostly for large values of the bare couplings. One-component
(`reduced') staggered fermions are used in a numerical simulation with the
Hybrid Monte Carlo algorithm. The fermion and Higgs masses and the renormalized
scalar field expectation value are computed on $L^3 24$ lattices, where $L$
ranges from $6$ to $16$. In the scaling region these quantities are found to
have a $1/L^2$ dependence, which is used to determine their values in the
infinite volume limit. We then calculate the $y_R$ and $\lambda_R$ from their
tree level definitions in terms of the masses and renormalized scalar field
expectation value, extrapolated to infinite volume. The scalar field
propagators can be described for momenta up to the cut-off by one fermion loop
renormalized perturbation theory and the results for $\lambda_R$ and $y_R$ come
out to be close to the tree level unitarity bounds. There are no signs that are
in contradiction with the triviality of the Yukawa and quartic self-coupling.
