  We argue for the existence of an upper bound $m_*$ on the Higgs mass at which
the lowest excited state of the Higgs field ceases to be the conventional plane
wave. An explicit construction of an alternative nonperturbative state is
discussed. This excitation is spatially localized. The field fluctuations
inside the localization region are large. The energy of the excitation is
smaller than the mass of the plane wave state $m$ at $m>m_*$. An approximate
value of $m_*$ is found to be $m_* \approx 4.75$ times the vacuum expectation
value. This is an upper bound at the tree level.
