In this article, we prove a structure theorem for unbounded operator valued local completely contractive map \(\psi \) defined on a unital locally \(C^{*}\) -algebra \(\mathcal {A}.\) There is a unique commutant operator T in the structure of \(\psi \) with norm at most 2. We show that the operator T is a contraction if and only if the block map \(\begin{aligned} \Phi =\begin{bmatrix} \varphi & \psi \\ \psi ^{*} & \varphi \end{bmatrix} \end{aligned}\) is local completely positive, for some local completely positive and local completely contractive map \(\varphi \) on \(\mathcal {A}.\) In general, such a map \(\varphi \) may not exist for a given \(\psi \) , we illustrate this situation with an example. However, we prove a block representation of \(\psi \) in the sense that there always exist a local completely positive and local completely bounded map \(\varphi \) such that \(\Phi \) is a local completely positive map.
