Let G be a connected graph, and let f be a function mapping V (G) into N. We define f(H)  = ∑ v∈V (H) f(v) for each subgraph H of G. The function f is called an IC-coloring of G if for each integer k in the set {1, 2,  ·  ·  · , f(G)} there exists an (induced) connected subgraph H of G such that f(H)  = k, and the IC-index of G, M(G), is the maximum value of f(G) where f is an IC-coloring of G. In this paper, we show that M(Km,n)  = 3 · 2m+n−2 − 2m−2 + 2 for each complete bipartite graph Km,n, 2 ≤ m ≤ n. 