Catholic Encyclopedia: „In case of necessity, baptism can be administered lawfully and validly by any person whatsoever who observes the essential conditions, whether this person be a Catholic layman or any other man or woman, heretic or schismatic, infidel or Jew.“
The essential conditions are that the person pour water upon the one to be baptized, at the same time pronouncing the words: „I baptize thee in the name of the Father and of the Son and of the Holy Ghost. Moreover, he must thereby intend really to baptize the person, or technically, he must intend to perform what the Church performs when administering this sacrament.“
The inability of the churches mutually to recognize their various practices of baptism as sharing in the one baptism, and their actual dividedness in spite of mutual baptismal recognition, have given dramatic visibility to the broken witness of the Church. The readiness of the churches in some places and times to allow differences of sex, race, or social status to divide the body of Christ has further called into question genuine baptismal unity of the Christian community (Gal. 3:27-28) and has seriously compromised its witness. The need to recover baptismal unity is at the heart of the ecumenical task as it is central for the realization of genuine partnership within the Christian communities.Lima-Erklärung Taufe (englisch) (Memento vom 9. Juli 2008 im Internet Archive)