The analysis of air bubbles trapped in polar ice has permitted the reconstruction of past atmospheric concentrations of CO2 over various timescales, and revealed that large climate changes over tens of thousands of years are generally accompanied by changes in atmospheric CO2 concentrations(1). But the extent to which such covariations occur for fast, millennial-scale climate shifts, such as the Dansgaard-Oeschger events recorded in Greenland ice cores during the last glacial period(2), is unresolved; CO2 data from Greenland(3) and Antarctic(4) ice cores have been conflicting in this regard, More recent work suggests that Antarctic ice should provide a more reliable CO2 record, as the higher dust(5) content of Greenland ice can give rise to artefacts(1,6,7). To compare the rapid climate changes recorded in the Greenland ice with the global trends in atmospheric CO2 concentrations as recorded in the Antarctic ice, an accurate common timescale is needed. Here we provide such a timescale for the last glacial period using the records of global atmospheric methane concentrations from both Greenland and Antarctic ice. We find that the atmospheric concentration of CO2 generally varied little with Dansgaard-Oeschger events (<10 parts per million by volume, p.p.m.v.) but varied significantly with Heinrich iceberg-discharge events (similar to 20 p.p.m.v.), especially those starting with a long-lasting Dansgaard-Oeschger event.