The second controversy of his episcopate was about baptism performed outside the church. In Africa the settled view, which Cyprian defended, was that such a baptism was simply not a baptism, because the one who administers it has nothing to give; a convert coming from a schismatic group was therefore baptised, not received. Stephen, bishop of Rome, held the opposite, that the rite was valid whoever performed it and that the convert should be received by the laying on of hands. The exchange became sharp, and Stephen is reported to have refused to receive the African envoys.
Neither man lived to settle it. Stephen died in 257 and Cyprian was beheaded in 258 under Valerian, after a first sentence of exile. The proconsular record of his trial, terse and procedural, survives, and it is one of the better documents of a Roman magistrate handling a Christian bishop.
The quarrel then outlived them both in a way neither would have wanted. A century later the Donatists cited Cyprian, correctly, for the position that sacraments administered by the unworthy are void, and Augustine had to argue against the most revered figure in African Christianity by distinguishing the validity of a rite from its fruitfulness. That distinction became standard Western doctrine, and it was reached under pressure from a schism.