  The production of the Standard Model Higgs boson in the four-fermion reaction
$e^+ e^- \to \mu^+ \mu^- b \bar b$ is studied. The complete tree-level matrix
element, including signal and backgrounds in the standard electroweak theory,
is computed and initial state radiation is taken into account in the
leading-log approximation. A Monte Carlo event generator has been built and
numerical results for some distributions of experimental interest for the
search of the Higgs particle at future electron-positron colliders are shown,
compared with those existing in the literature and commented.
