The energy shifts of optical interband transition edges, E'0, E1, E1+Δ1 and E2, of relaxed Si1-xGex alloys grown epitaxially on Si(001) substrates by molecular beam epitaxy have been studied as a function of Ge composition using their complex dielectric functions measured by spectroscopic ellipsometry at room temperature. The interband transition edges were resolved by a line shape fitting on the ... [Show full abstract] numerical second derivative spectra of the dielectric functions. The E'0, E1, E1+Δ1 and E2(Σ) edges are found to shift to lower energies with increasing Ge composition while the E2(X) edge shifts to higher energies. Also it is found for E1 and E1+Δ1 energies that downward bowing exists and for Δ1 energy that upward bowing exists. These behaviours of the transition edges are understood by comparing the band structure of Si with that of Ge and interpreted as due to the effect of the random potential originated by alloying disorder.