  An upperbound on the mass of the lightest neutral scalar Higgs boson is
calculated in an extended version of the minimal supersymmetric standard model
that contains an additional Higgs singlet. We integrate the renormalization
group equations of the model, and impose low energy boundary conditions
consistent with present experimental results, and ultra-violet conditions
following from triviality. Radiative corrections induced by a large top quark
Yukawa coupling are included in our analysis, and we find the allowed values
for the mass of the Higgs boson as a function of the mass of the top quark.
Typically, for a top quark mass $m_t=150\ GeV$, the upper bound on the Higgs
boson mass is about $25 \ GeV$ higher than in the minimal model.
