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A coloring of the edges of a graph G is strong if each color class is an induced matching of G. The strong chromatic index of G, denoted by χ_s^'(G), is the least number of colors in a strong edge coloring of G. In this note we prove that χ_s^'(G)≤ (4k-1)Δ (G)-k(2k+1)+1 for every k-degenerate graph G. This confirms the strong version of conjecture stated recently by Chang and Narayanan . Our approach allows also to improve the upper bound from  for chordless graphs. We get that boundsarXiv:1301.1992v1 fatcat:olsn5rpujjgdfcuh7y327so7yq