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General arguments related to ``triviality'' predict that, in the broken phaseof $(\lambda\Phi^4)_4$ theory, the condensate $<\Phi>$ re-scales by a factor$Z_{\phi}$ different from the conventional wavefunction-renormalization factor,$Z_{prop}$. Using a lattice simulation in the Ising limit we measure$Z_{\phi}=m^2 \chi$ from the physical mass and susceptibility and $Z_{prop}$from the residue of the shifted-field propagator. We find that the two $Z$'sdiffer, with the difference increasing rapidly as the continuum limit isapproached. Since $Z_{\phi}$ affects the relation of $<\Phi>$ to the Fermiconstant it can sizeably affect the present bounds on the Higgs mass.Comment: 10 pages, 3 figures, 1 table, Latex2

FIRST LATTICE EVIDENCE FOR A NONTRIVIAL RENORMALIZATION OF THE HIGGS CONDENSATE