Zipserite is a new mineral species discovered in a sample collected from the old mine dumps of the abandoned epithermal deposit Nagybörzsöny in Hungary. Zipserite occurs as anhedral to subhedral, lath-like grains, up to 500 μm in size, in hydrothermally strongly altered rocks. It is found at a contact between bismuth and bismuthinite, also associated with rare ikunolite and joséite-A. Zipserite is silvery white with a metallic lustre. Mohs hardness is ca. 2–3 and the calculated density is 7.815 g.cm–3. In reflected light, zipserite is grey–white, with colour and reflectance essentially matching those of bismuthinite. Bireflectance is weak, internal reflections not present. Anisotropy is moderately strong, with dark blue and grey colours of anisotropy. Reflectance values for the four Commission on Ore Mineralogy wavelengths of zipserite in air [Rmax, Rmin (%) (λ in nm)] are: 48.4, 46.4 (470); 47.8, 45.9 (546); 47.8, 45.8 (589); and 47.5, 45.6 (650). The empirical formula, based on electron-microprobe analyses, is (Bi4.74Pb0.31)Σ5.05(S3.38Se0.56Te0.02)Σ3.96, that can be simplified as Bi5(S,Se)4. The ideal end-member formula of zipserite is Bi5S4, which requires Bi 89.07 and S 10.93, total 100 wt.%. Zipserite possesses a fascinating crystal structure. The average structure is trigonal, with space group P$\bar{3}$m, a = 4.162(1) Å, c = 16.397(1) Å, V = 245.94(4) Å3 and Z = 2. The structure is built by the alternation of a double bismuth layer Bi2 and the Bi3S4 block which is a three octahedra thick layer. Its general formula can be expressed as Bi2 + Bi3S4, which corresponds directly to the observed stacking. At 98 K, the structure can be described using the superspace formalism with an R-centred trigonal unit cell a = 4.209(2) Å, c0 = 5.616(6) Å, a modulation vector q ≈ 4/3 c* and the superspace group R$\bar{3}$m(00γ)00. Zipserite is not only a new mineral but also the first named member of a new sub-group of compounds within the broader family of bismuth chalcogenides, characterised by complex stacking of structural units (Bi2 layers and Bi3S4 blocks). Some of these phases are being investigated as promising thermoelectric materials and synthetic analogues of zipserite could also be inspected for similar physical properties.