Abrupt transitions between cold/dry stadial and warm/wet interstadial states occurred during glacial periods in the absence of any known external forcing. The climate record preserved in polar glaciers, mountain glaciers, and widespread cave deposits reveals that these events were global in extent with temporal distribution implying an underlying memoryless process with millennial time scale. Here a theory is advanced implicating feedback between atmospheric dust and the hydrological cycle in producing these abrupt transitions. Calculations are performed using a radiative-convective model that includes the interaction of aerosols with radiation to reveal the mechanism of this dust/precipitation interaction feedback process and a Langevin equation is used to illustrate glacial climate destabilization by this mechanism. This theory explains the observed abrupt, bimodal, and memoryless nature of these transitions as well as their intrinsic connection with the hydrological cycle.