Four compounds of the Bi₄Ti₃O₁₂/BiFeO ₃ system with the formula Bi₂Bi_n-1(Ti,Fe) _nO_3n+3, n = 3, 4, 4.5 and 6 were studied using high-temperature X-ray powder diffraction and differential thermoanalysis methods. The crystal structure of the n = 6 phase was refined by the Rietveld method. An unusual behaviour of thermal expansion attributed to an orthorhombic-to-tetragonal transformation was revealed. For all the compounds, the lattice parameter c vs temperature T dependence has three regions in the range of T = 20 -750°C interpreted as (1) expansion of the initial orthorhombic phase, (2) a pronounced structure reconstruction to the tetragonal phase, (3) an expansion of the tetragonal phase. The crystal structure of Bi₇Ti₃Fe₃O₂₁ based on 6-layer-perovskite blocks is proposed from X-ray powder diffraction data. The Rietveld refinement of the structure in the orthorhombic space group F2mm with lattice parameters a = 5.4699(3), b = 5.4924(3), c = 57.551(3) Å (R _p = 9.4, R_wp = 11.9, R_exp = 4.7, R_B = 4.4%) shows that a distorted 6-layer model fits the data of Bi ₇Ti₃Fe₃O₂₁.