In 2009, Kong, Wang, and Lee introduced the problem of finding the edge-balance index sets (EBI) of complete bipartite graphs, \(K_{m,n}\) , by examining the cases \(n=1\) , 2, 3, 4, 5, and the case \(m=n\) . Since then, the problem of finding \(EBI(K_{m,n})\) , where \(m \geq n\) , has been completely resolved for the case where m is odd and n is even, and for the two cases where m and n have the same parity. In this paper, we find the edge-balance index sets for complete bipartite graphs where m is even and n is odd, thereby concluding the problem of finding the edge-balance index sets for all complete bipartite graphs.