  We study the vacuum stability of the singlet Majoron model using full
renormalization group improved scalar potential and Monte Carlo techniques. We
show that in the perturbative regime of the various free parameters, the vacuum
stability requirement together with LEP limits is passed by 18% of the
parameter space if the scale of new physics is 10 TeV and 6% if the scale is
$10^{14}$ GeV. Moreover, if the baryogenesis condition for scalar couplings is
required, no portion of the parameter space survives.
