A new A(n)B(n)O(3n-2) homologous series of anion-deficient perovskites has been evidenced by preparation of the members with n = 5 (Pb(2.9)Ba(2.1)Fe(4)TiO(13)) and n = 6 (Pb(3.8)Bi(0.2)Ba(2)Fe(4.2)Ti(1.8)O(16)) 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, R(I) = 0.035, R(P) = 0.042 for Pb(2.9)Ba(2.1)Fe(4)TiO(13) and S.G. Imma, a = 5.7199(1), b = 3.97066(7), c = 32.5245(8) Å, R(I) = 0.032, R(P) = 0.037 for Pb(3.8)Bi(0.2)Ba(2)Fe(4.2)Ti(1.8)O(16)). 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 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 Mössbauer spectroscopy reveal that Pb(2.9)Ba(2.1)Fe(4)TiO(13) and Pb(3.8)Bi(0.2)Ba(2)Fe(4.2)Ti(1.8)O(16) are antiferromagnetically ordered below T(N) = 407 and 343 K, respectively. The Pb(2.9)Ba(2.1)Fe(4)TiO(13) and Pb(3.8)Bi(0.2)Ba(2)Fe(4.2)Ti(1.8)O(16) compounds are in a paraelectric state in the 5-300 K temperature range.