The growth of Bi on a Si(001) surface is studied in situ by spot profile analyzing low-energy electron diffraction and ex situ by atomic force microscopy. A continuous epitaxial Bi(111) film with a thickness of 6 nm is grown at 150 K in a bilayer growth mode. During annealing to 450 K the lattice mismatch between Si(001) and Bi(111) is accommodated by a periodic interfacial misfit dislocation array. On this relaxed template, Bi(111) films can be grown to any desired thickness. Such films are composed of twinned and 90° rotated micrometer sized Bi(111) crystallites with a roughness of less than 0.6 nm for a 30 nm thick film.