The harmonic index of a graph is defined as the sum of the weights of all edges of , where denotes the degree of a vertex in . The chromatic number of is the smallest number of colors needed to color all vertices of in such a way that no pair of adjacent vertices get the same color. The main result in this paper is proved by using the effect of removal of a minimum degree vertex on the harmonic index. It strengthens a result relating the Randić index and the chromatic number obtained by the system AutoGraphiX and proved by Hansen and Vukicević.