Suppose G = (V,E) is a graph with vertex set V and edge set E. A vertex labeling f : V → {0, 1} induces an edge labeling f∗ : E → {0, 1} defined by f∗(xy) = |f(x) − f(y)|. For iϵ {0, 1}, let vf(i) and ef(i) be the number of vertices v and edges e with f(v) = i and f∗(e) = i, respectively. A graph G is cordial if there exists a vertex labeling f such that |vf(0) − vf(1)| ⩽ 1 and |ef(0) − ef(1)| ⩽ 1. This paper determines all m and n for which mKn is cordial.