In this letter, the effect of reversed magnetic domains of BaFe12O19 on superconductivity is investigated in Pb/BaFe12O19 hybrids. The critical field of the Pb film is increased by about 5 kOe due to the compensation of the applied field by the stray field above the reversed domains. Being related to smaller critical fields of Pb, at,fields near the saturation field of BaFe12O19, the superconductivity can only exist above the reversed domains even at low temperatures. As a consequence of the pure reversed domain superconductivity, magnetic-field-induced superconductivity is observed in a broad temperature range. (c) 2006 American Institute. of Physics.