Abstract. In a recent paper with L. Q. Zamboni the authors introduced the class of -episturmian words, where is an involutory antimorphism of the free monoid A . In this paper, we introduce and study characteristic morphisms, that is, morphisms which map standard episturmian words into standard -episturmian words. They are a natural extension of standard episturmian morphisms. The main result of the paper is a characterization of these morphisms when they are injective.