  The `triviality' of $\Phi^4_4$ has been traditionally interpreted within
perturbation theory where the prediction for the Higgs boson mass depends on
the magnitude of the ultraviolet cutoff $\Lambda$. This approach crucially
assumes that the vacuum field and its quantum fluctuations rescale in the same
way. The results of the present lattice simulation, confirming previous
numerical indications, show that this assumption is not true. As a consequence,
large values of the Higgs mass $m_H$ can coexist with the limit $\Lambda\to
\infty $. As an example, by extrapolating to the Standard Model our results
obtained in the Ising limit of the one-component theory, one can obtain a value
as large as $m_H=760 \pm 21$ GeV, independently of $\Lambda$.
