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We consider the possibility of Higgs boson detection at LEP II under the resonance threshold (\sqrt{s}<m_H+m_Z) in the framework of complete tree level approach to the calculation of the e^+ e^- \rightarrow \nu \bar \nu b \bar b amplitude, simulating b-quark fragmentation to hadrons and taking into account typical detector properties. At the energy below the 2m_Z threshold \sqrt{s}= 175 GeV Higgs boson production under the m_H+m_Z threshold is practically background free

HIGGS BOSON PRODUCTION UNDER THE RESONANCE THRESHOLD AT LEP II