Negative hydrogen ion (H-) sources employed in neutral beam injection (NBI) systems are subject to extraction efficiency issues due to the considerable volumetric losses of negative hydrogen ions. Here, we propose to improve the H- extraction by activating an alternative sheath mode, the electronegative inverse sheath, in front of the H- production surface, which features zero sheath acceleration for H- with a negative sheath potential opposite to the classic sheath. With the inverse sheath activated, the produced H- exhibits smaller gyration, a shorter transport path, less destructive collisions, and therefore higher extraction probability than the commonly believed space-charge-limited (SCL) sheath. Formation of the proposed electronegative inverse sheath and the SCL sheath near the H--emitting surface is investigated by the continuum kinetic simulation. Dedicated theoretical analyses are also performed to characterize the electronegative inverse sheath properties, which qualitatively agree with the simulation results. We further propose that the transition between the two sheath modes can be realized by tuning the cold ion generation near the emissive boundary. The electronegative inverse sheath is always coupled with a plasma consisting of only hydrogen ions with approximately zero electron concentration, which is reminiscent of the ion-ion plasma reported in previous NBI experiments.