Climate in the early Pleistocene varied with a period of 41 kyr and was related to variations in Earth's obliquity. About 900 kyr ago, variability increased and oscillated primarily at a period of approximately 100 kyr, suggesting that the link was then with the eccentricity of Earth's orbit. This transition has often been attributed to a nonlinear response to small changes in external boundary conditions. Here we propose that increasing variablility within the past million years may indicate that the climate system was approaching a second climate bifurcation point, after which it would transition again to a new stable state characterized by permanent mid-latitude Northern Hemisphere glaciation. From this perspective the past million years can be viewed as a transient interval in the evolution of Earth's climate. We support our hypothesis using a coupled energy-balance/ice-sheet model, which furthermore predicts that the future transition would involve a large expansion of the Eurasian ice sheet. The process responsible for the abrupt change seems to be the albedo discontinuity at the snow-ice edge. The best-fit model run, which explains almost 60% of the variance in global ice volume during the past 400 kyr, predicts a rapid transition in the geologically near future to the proposed glacial state. Should it be attained, this state would be more 'symmetric' than the present climate, with comparable areas of ice/sea-ice cover in each hemisphere, and would represent the culmination of 50 million years of evolution from bipolar nonglacial climates to bipolar glacial climates.