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We present an algorithm for omputing the pre x of an automaton. Automata onsidered are non-deterministi , labelled on words, and an have "-transitions. The pre x automaton of an automaton A has the following hara teristi properties. It has the same graph as A. Ea h a epting path has the same label as in A. For ea h state q, the longest ommon pre x of the labels of all paths going from q to an initial or nal state is empty. The interest of the omputation of the pre x of an automaton is that it is the rst step of the minimization of sequential transdu ers. The algorithm that we des ribe has the same worst ase time omplexity as another algorithm due to Mohri but our algorithm allows automata that have empty labelled y les. If we denote by P (q) the longest ommon pre x of labels of paths going from q to an initial or nal state, it operates in time O((P + 1) jEj) where P is the maximal length of all P (q).