Effects of quenched disorder on a coupled map model of earthquakes are studied. In its original version, this model is known to display a self-organized critical distribution of avalanches. However, when some finite amount of quenched disorder is introduced, the bulk sites synchronize fully and a single stable system-wide avalanche appears. This synchronization is found for a wide band of disorder and goes against some recent predictions about integrate-and-fire models. {copyright} {ital 1996 The American Physical Society.}