The largest uncertainty in the ice sheet models used to predict future sea level rise originates from our limited understanding of processes at the ice/bed interface. Near glacier termini, where basal sliding controls ice flow, most predictive ice sheet models use a parameterization of sliding that has been theoretically derived for glacier flow over a hard bed. We find that this sliding relation does not apply to the 140 Greenland glaciers that we analyzed. There is no relationship between basal sliding and frictional stress at the glacier bed, contrary to theoretical predictions. There is a strong relationship between sliding speed and net pressure at the glacier bed. This latter finding is in agreement with earlier observations of mountain glaciers that have been largely overlooked by the glaciological community.