  We study the stability of the Electroweak (EW) vacuum in a scale-invariant
extension of the Standard Model and General Relativity, known as a
Higgs-Dilaton theory. The safety of the EW vacuum against possible transition
towards another vacuum is a necessary condition for the model to be
phenomenologically acceptable. We find that, within a wide range of parameters
of the theory, the decay rate is significantly suppressed compared to that of
the Standard Model. We also discuss properties of a tunneling solution that are
specific to the Higgs-Dilaton theory.
