A structural analysis of the double-collapsed-phase Bi6+xSr9-xFe5O26 is presented in light of the modulated-phase Bi2.4Sr2.6Fe2O9+delta previously investigated [Y. Lepage, W. R. McKinnon, J. M. Tarascon, and P. Bar boux, Phys. Rev. B 40, 6810 (1989); O. Perez, W. LeIigny, D. Grebille, J. M. Greneche, Ph. Labbe, D. Groult, and B. Raveau, Phys. Rev. B 55, 1236 (1997)]. The study was carried out on a single crystal, using synchrotron radiation (lambda = 0.326 Angstrom). The crystal is monoclinic with cell parameters a = 16.491(9) Angstrom, b = 5.481(3) Angstrom, c = 30.086(16) Angstrom, beta = 91.39(2)degrees. The real structure of symmetry P2(1)/n appears as a small perturbation of the ideal structure with higher symmetry B2/m. The undulating (001)(m) layers of the modulated (m) phase built from one kind of cation (Bi, Sr, or Fe) are replaced by mixed layers. The waving of these layers is less regular than in the modulated phase because interrupted layers are connected. One of the most interesting results relates to the interrupted Bi layers: the isolated blocks composed of two adjacent infinite [010] ribbons, six Bi atoms wide, are similar to the ordered part (condensed zones) of the Bi-2212 modulated phase. The Bi disordered regions (diluted zones) are missing in the double-collapsed phase. An original octahedral coordination is implied for the Bi atoms located near the Fe atoms in the same undulated mixed layer. Disorder phenomena have been observed in a complementary HREM study and appear as localized faults modifying mainly the length of the Bi ribbons.