An H-magic labeling in an H-decomposable graph G is a bijection f:V(G) U E(G) --> {1,2, … ,p+q} such that for every copy H in the decomposition, $\sum\limits_{v\in V(H)} f(v)+\sum\limits_{e\in E(H)} f(e)$ is constant. The function f is said to be H-E-super magic if f(E(G)) = {1,2, … ,q}. In this paper, we study some basic properties of m-factor-E-super magic labelingand we provide a necessary and sufficient condition for an even regular graph to be 2-factor-E-super magic decomposable. For this purpose, we use Petersen's theorem and magic squares.