For the first time the structure of the polycristalline alpha - Bi4V2O11 low-temperature form has been determined by Rietveld analysis using X-ray and neutron diffraction data in the C2/m space group. Although this phase was previously claimed to be orthorhombic, it is actually monoclinic as we deduced from XRPD patterns. The true cell arises from a six-fold commensurate modulation of the orthorhombic mean cell along the c(M) monoclinic axis, but because of the weakness of the intensity of some diffraction lines due to the six-fold superstructure, only the three-fold could be investigated. alpha - Bi4V2O11 is structurally related to the parent Aurivillius prototype. However the perovskite layers with composition (VO3.5square0.5)2- which interleave the (Bi2O2)2+ slabs are broken into files made up of alternating vanadium - oxygen tetrahedra and oxygen-deficient octahedra, running along the modulation c(M) axis. The one-dimensional modulation depends on oxygen long-range ordering and can be viewed as resulting from coupled valence modulations of both vanadium and bismuth cations.