The edge-bandwidth of a graph \( G \) is the smallest number \( b \) for which there exists an injective labeling of \( E(G) \) with integers such that the difference between the labels of any pair of adjacent edges is at most \( b \). The edge-bandwidth of a torus (a product of two cycles) has been computed within an additive error of \( 5 \). In this paper, we improve the upper bound, reducing the error to \( 3 \).