We investigate the molecular-beam-epitaxy growth of highly relaxed Si0.45Ge0.55 films with very low dislocation densities. By using the Si3N4 film as the mask material, the Si0.45Ge0.55 film can be grown on a compositionally stepwise graded SiGe buffer layer in 3μm×3μm windows on a Si (001) substrate. Raman scattering spectroscopy measurement shows that more than 90% strain of the Si0.45Ge0.55 film is relaxed, and almost neither misfit dislocation lines nor etch pits of thread dislocations could be observed when the sample is etched by the modified Schimmel etchant. We suggest that the results can be explained by influence of the edge-induced strain relaxation of the epitaxial film and the edge-induced stress of the mask material.