The basic and the charge density wave (CDW) structures of the monoclinic NbS3-II polymorph were studied by synchrotron x-ray diffraction, ab-initio calculation, simulation of electron diffraction patterns and by atomicresolution transmission electron and low-temperature scanning tunneling microscopies. It is shown that the basic structure belongs to the space group P 21/m and is described with a unit cell, formed of four pairs of symmetry-related trigonal prismatic (TP) columns (a0 = 0.96509(8) nm, b0 = 0.33459(2) nm, c0 = 1.9850(1) nm, β0 = 110.695(4) • ), with all Nb and S atoms in 2e special positions. The two CDWs, with q1 = (0, 0.298,0) and q2 = (0, 0.352, 0), form their own modulation unit cells (am = 2a0, bm = b0/qjb, cm = c0, βm = β0) and are ordered pairwise along adjacent isosceles TP columns. The symmetries of both qj modes belong to the space group Cm and are related according to the 2a special positions. If considered as long-period commensurate, the entire modulated structure with both CDWs included is best described with an enlarged unit cell (a = 2a0, b = 37b0, c = c0, β = β0), with all Nb and S atoms in 1a positions of the space group P 1.