Vaidya and Barasara proposed the concept of edge product cordial labeling. This motivates us to define a new labeling called -square product E-cordial labeling which is defined as follows: Let G(V,E) be a simple graph. A labeling f:E(G)→{1,2,3,4} with induced labeling f^*:V(G)→{0,1} defined by f^* (v)=∏▒〖{〖 f(uv)〗^2/uv∈E(G)}(mod 2).〗 The labeling f is called 4-square product E-cordial labeling if |v_f (0)-v_f (1)|≤1 and |e_f (i)-e_f (j)|≤1 where v_f (0) and v_f (1) is the number of vertices labeled with 0 and 1 respectively; e_f (i) and e_f (j) is the number of edges labeled with i and j respectively. A graph which admits 4-square product E-cordial labeling is called 4-square product E-cordial graph.