We present an L 2 integrable method with B-spline basis to describe the electronic continuum of two-electron diatomic molecules. The method is applied to obtain (i) energy positions and widths of the lowest 1 + u doubly-excited states of the H 2 molecule, and (ii) photoionization cross sections of H 2 in the fixed-nuclei approximation. Our results are compared with existing theoretical and experimental works. We show the existence of avoided crossings between two series of doubly-excited states, (2pσ u nsσ g ) and (2pσ u ndσ g ), converging to the 2pσ u ionization threshold of H 2 .