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Let G be an outerplane graph with maximum degree △ and the entire chromatic number χvef (G). This paper proves that if △≥ 6, then △ + 1 ≤χvef (G) ≤△ + 2,and χvef (G) = △ + 1 if and only if G has a matching M consisting of some inner edges which covers all its vertices of maximum degree.