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Oxygen isotope records from Chinese caves characterize changes in both the Asian monsoon and global climate. Here, using our new speleothem data, we extend the Chinese record to cover the full uranium/thorium dating range, that is, the past 640,000 years. The record's length and temporal precision allow us to test the idea that insolation changes caused by the Earth's precession drove the terminations of each of the last seven ice ages as well as the millennia-long intervals of reduced monsoon rainfall associated with each of the terminations. On the basis of our record's timing, the terminations are separated by four or five precession cycles, supporting the idea that the '100,000-year' ice age cycle is an average of discrete numbers of precession cycles. Furthermore, the suborbital component of monsoon rainfall variability exhibits power in both the precession and obliquity bands, and is nearly in anti-phase with summer boreal insolation. These observations indicate that insolation, in part, sets the pace of the occurrence of millennial-scale events, including those associated with terminations and 'unfinished terminations'.