\(^{20}\)Ne has been known as a typical example of a nucleus with \(\alpha\) cluster structure (\(^{16}\)O+\(\alpha\) structure). However according to the spherical shell model, the spin-orbit interaction acts attractively for four nucleons outside of the \(^{16}\)O core, and this spin-orbit effect cannot be taken into account in the simple \(\alpha\) cluster models. We investigate how the \(\alpha\) cluster structure competes with independent particle motions of these four nucleons. The antisymmetrized quasi-cluster model (AQCM) is a method to describe a transition from the \(\alpha\) cluster wave function to the \(jj\)-coupling shell model wave function. In this model, the cluster-shell transition is characterized by only two parameters; \(R\) representing the distance between clusters and \(\Lambda\) describing the breaking of \(\alpha\) clusters, and the contribution of the spin-orbit interaction, very important in the \(jj\)-coupling shell model, can be taken into account by changing \(\alpha\) clusters to quasi clusters. In this article, based on AQCM, we apply \(^{16}\)O plus one quasi cluster model for \(^{20}\)Ne. Here we focus on the \(E0\) transition matrix element, which has been known as the quantity characterizing the cluster structure. The \(E0\) transition matrix elements are sensitive to the change of the wave functions from \(\alpha\) cluster to \(jj\)-coupling shell model.