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 letters
in such a way that it remains morphic and Sturmian.
Yasutomi (1997) has proved that these were the sole possible additions and
that, 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.
