A new A(n)B(n)O(3-n) 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= 26.83780(4) angstrom, R-I= 0.035, R-P = 0.042 for Pb2.9Ba2.1Fe4TiO13 and S.G. Imma, a = 5.7199(1), b = 3.97066(7), c = 32.5245(8) angstrom, R-I = 0.032, R-P = 0.037 for Pb3.813i0,2Ba2Fe4,2Ti1.8016). The crystal structures of the A(n)B(n)O(3n-2) homologues are formed by slicing the perovskite structure with (101)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 edgesharing 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 Mossbauer 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.