Among Sturmian words, some of them are morphic, i.e. fixed point of a non-identical morphism on words. Berstel and Séébold (1993) have shown that if a characteristic Sturmian word is morphic,then it can be extended by the left with one or two lettersin such a way that it remains morphic and Sturmian.Yasutomi (1997) has proved that these were the sole possible additions andthat, if we cut the first letters of such a word, it didn't remain morphic.In this paper, we give an elementary and combinatorial proof of this result.