Cubic boron nitride (c-BN), although offering a number of highly attractive properties comparable to diamond, like hardness, chemical inertness and a large electronic bandgap, up to now has not found the attention it deserves. This mostly has to do with preparational problems, with easy chemical routes not available and, instead, the necessity to apply ion-bombardment-assisted methods. Hence, most of the c-BN samples prepared as thin films have been nanocrystalline, making the prospect of using this material for high-temperature electronic applications an illusion. Although heteroepitaxial nucleation of c-BN on diamond substrates has been demonstrated using the high-pressure-high-temperature technique, none of the low-pressure methods ever succeeded in the epitaxial growth of c-BN on any substrate. Here, we demonstrate that heteroepitaxial c-BN films can be prepared at 900 degrees C on highly (001)-oriented diamond films, formed by chemical vapour deposition, using ion-beam-assisted deposition as a low-pressure technique. The orientation relationship was found to be c-BN(001)[100]||diamond(001)[100]. High-resolution transmission electron microscopy additionally proved that epitaxy can be achieved without an intermediate hexagonal BN layer that is commonly observed on various substrates.