The modulation of the lazurite structure has been determined by X-ray diffraction methods. The indexing of satellites on X-ray diffraction powder patterns has been made by means of single crystal X-ray diffraction patterns. The irrationality of the satellite distance from the basic reflections in some specimens of isotropic lazurite confirms the incommensurability of the wavelength of modulation by an edge magnitude of the sodalite subcell and the necessity of a fractional mineral lattice. X-ray diffraction powder data of lazurites with different periods of incommensurate-modulated structure are established. Modulation structure parameters are 0.217 and 0.175, respectively. Indexing of X-ray diffraction powder data of cubic Baikal lazurite suggested by the PDF editorial staff is considered.