Deposition of boron nitride thin films containing considerable amounts of the cubic phase has already been accomplished on numerous different substrate materials. However, only for single-crystal silicon substrates is detailed knowledge of the film structure yet available. In this work, boron nitride thin films with maximum cubic phase content have been deposited by RF magnetron sputtering of a h-BN target on fused silica substrate. The film structure was investigated by cross-section high-resolution transmission electron microscopy (X-HRTEM) and electron energy loss spectroscopy (EELS). Both the growth conditions for optimum c-BN formation and the film structure were essentially the same as for deposition on silicon substrates, in spite of certain structural peculiarities of those films reported in the literature.