In this paper we construct a natural filtration associated to the plethysm $S_{r}(wedge^2 varphi)$ over arbitrary commutative ring R. Let $phi$ : G longrightarrow F be a morphism of finite free R-modules. We construct the natural filtration of $S_{r}(wedge^2 varphi)$ as a $GL(F){ imes}GL(G)$- complex such that its associated graded complex is ${Sigma}_{{lambda}{in}{Omega}_{gamma}}=L_{2{lambda}{varphi}$, where ${{Omega}_{gamma}}^{-}$ is a set of partitions such that $│wedge│;=;{gamma};and;2{wedge}$ is a partition of which i-th term is $2{wedge}_{i}$. Specializing our result, we obtain the filtrations of <TEX>$S_{r}(wedge^2 F);and;D_{r}(D_2G).