Some properties on primary automata are studied in this paper. Firstly, the endomorphism of the primary automaton is dealt with. The paper proves that if all the primary automata are S(orG)automaton, so is . Secondly, the union of the strongly connected automata is proved to be Gautomaton. Finally, the definition of canonical automata is extent to finite automata by the minimal generated set. Also, the definition of generalized canonical automata is given and the sufficient conditions are provided.