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

Probing Higgs self-coupling of a classically scale invariant model in $e^+e^- \to Zhh$: Evaluation at physical point