  Since the TRIVIALITY argument of the Higgs sector requires the existence of
new physics beyond the standard model, there should exist a cutoff $\Lambda$
beyond which the standard model will breakdown. The cutoff can be determined
from the position of the Landau pole. We study the effects of this cutoff on
the energy of the electroweak sphaleron, $E^{spha}$, in the large Higgs boson
mass limit. We found that $E^{spha}$ becomes arbitrarily large as the Higgs
boson mass increases. This is in contrast to the well-known result, which is
held in the standard model and a wide class of its extensions, that $E^{spha}$
is stable against the variation of the {\it bare} Higgs boson mass. The
physical meaning of this result is discussed.
