In this article, we show that under certain assumptions every multiplicative Lie triple higher derivation L= {Li}i∈N on U is of standard form, i.e., each component Li has the form Li = δi + γi, where {δi}i∈N is an additive higher derivation on U and {γi}i∈N is a sequence of mappings γi : U → Z(U) vanishing at Lie triple products on U.