  A classically scale invariant extension of the standard model predicts large
anomalous Higgs self-interactions. We compute missing contributions in previous
studies for probing the Higgs triple coupling of a minimal model using the
process $e^+e^- \to Zhh$. Employing a proper order counting, we compute the
total and differential cross sections at the leading order, which incorporate
the one-loop corrections between zero external momenta and their physical
values. Discovery/exclusion potential of a future $e^+e^-$ collider for this
model is estimated. We also find a unique feature in the momentum dependence of
the Higgs triple vertex for this class of models.
