  The complete matrix element for $e^+e^-\ar b\bar bZ^0Z^0$ has been computed
at tree--level and applied to $Z^0H^0$--production followed by $Z^0\ar b\bar b$
and $H^0\ar Z^0Z^0$, including all the irreducible background, at Next Linear
Colliders. We find that, assuming flavour identification of the $Z^0$--decay
products, this channel, together with $e^+e^-\ar b\bar bW^+W^-$ in which
$Z^0H^0\ar (b\bar b)(W^+W^-$), can be important for the study of the parameters
of the Standard Model Higgs boson over the heavy mass range $2M_{Z^0}\Ord
M_{H^0}\Ord 2{m_t}$.
