When St. Augustine chose to write against a contemporary heretic group he had to address the question of re-baptism. The Donatists felt that only they could baptize Christians and all other baptisms were invalid. If a Donatist chose to reenter the Catholic Church do they need to be re-baptized? St Augustine decided that the Donatists were wrong and so he wrote that all baptisms were valid and there was no need for re-baptism. ANYONE can baptize someone as long as they followed the correct procedure. That policy remains to this day. The Catholics feel that the baptism really doesn’t have any meaning unless you are a member of the church but if you got baptized and then entered the Church you do not need to be re-baptized.

(The Great Courses – Augustine: Philosopher and Saint)