Abstract: A new AnBnO3n−2 homologous series of anion-deficient perovskites has been evidenced by preparation of the members with n = 5 (Pb2.9Ba2.1Fe4TiO13) and n = 6 (Pb3.8Bi0.2Ba2Fe4.2Ti1.8O16) in a single phase form. The crystal structures of these compounds were determined using a combination of transmission electron microscopy and X-ray and neutron powder diffraction (S.G. Ammm, a = 5.74313(7), b = 3.98402(4), c = 26.8378(4) Å, RI = 0.035, RP = 0.042 for Pb2.9Ba2.1Fe4TiO13 and S.G. Imma, a = 5.7199(1), b = 3.97066(7), c = 32.5245(8) Å, RI = 0.032, RP = 0.037 for Pb3.8Bi0.2Ba2Fe4.2Ti1.8O16). The crystal structures of the AnBnO3n−2 homologues are formed by slicing the perovskite structure with (01)p crystallographic shear (CS) planes. The shear planes remove a layer of oxygen atoms and displace the perovskite blocks with respect to each other by the 1/2[110]p vector. The CS planes introduce edge-sharing connections of the transition metal−oxygen polyhedra at the interface between the perovskite blocks. This results in intrinsically frustrated magnetic couplings between the perovskite blocks due to a competition of the exchange interactions between the edge- and the corner-sharing metal−oxygen polyhedra. Despite the magnetic frustration, neutron powder diffraction and Mssbauer spectroscopy reveal that Pb2.9Ba2.1Fe4TiO13 and Pb3.8Bi0.2Ba2Fe4.2Ti1.8O16 are antiferromagnetically ordered below TN = 407 and 343 K, respectively. The Pb2.9Ba2.1Fe4TiO13 and Pb3.8Bi0.2Ba2Fe4.2Ti1.8O16 compounds are in a paraelectric state in the 5−300 K temperature range.