The development of two-dimensional (2D) materials has opened up possibilities for their application in electronics, optoelectronics and photovoltaics, because they can provide devices with smaller size, higher speed and additional functionalities compared with conventional silicon-based devices(1). The ability to grow large, high-quality single crystals for 2D components-that is, conductors, semiconductors and insulators-is essential for the industrial application of 2D devices(2-4). Atom-layered hexagonal boron nitride (hBN), with its excellent stability, flat surface and large bandgap, has been reported to be the best 2D insulator(5-12). However, the size of 2D hBN single crystals is typically limited to less than one millimetre(13-18), mainly because of difficulties in the growth of such crystals; these include excessive nucleation, which precludes growth from a single nucleus to large single crystals, and the threefold symmetry of the hBN lattice, which leads to antiparallel domains and twin boundaries on most substrates(19). Here we report the epitaxial growth of a 100-square-centimetre single-crystal hBN monolayer on a low-symmetry Cu (110) vicinal surface, obtained by annealing an industrial copper foil. Structural characterizations and theoretical calculations indicate that epitaxial growth was achieved by the coupling of Cu < 211 > step edges with hBN zigzag edges, which breaks the equivalence of antiparallel hBN domains, enabling unidirectional domain alignment better than 99 per cent. The growth kinetics, unidirectional alignment and seamless stitching of the hBN domains are unambiguously demonstrated using centimetre-to atomic-scale characterization techniques. Our findings are expected to facilitate the wide application of 2D devices and lead to the epitaxial growth of broad non-centrosymmetric 2D materials, such as various transition-metal dichalcogenides(20-23), to produce large single crystals.