A technique employing inclined beams of electrons and ions has been developed and used to measure cross sections of the reaction H^-+e to H+2e for interaction energies between threshold (0.75 eV) and 30 eV. the magnitudes of the cross sections agree closely with results which Peart et al. obtained, for energies greater than 12.5 eV, with normally inclined beams. At energies close to 14.2 eV a pronounced structure has been observed in the detachment cross section. This could be attributed to the formation of a state of H^2- with a lifetime of order 10^-15 s.