On May 21st, 2003, a Mw = 6.8 earthquake struck the central part of northern Algeria causing extensive damage in the Boumerdes area, 40 km east of Algiers. It is among the largest events to occur in the western Mediterranean over the past 25 years. We present GPS measurements of horizontal coseismic displacements that provide new constraints on the rupture geometry. Modeling the data with a uniform dislocation on a rectangular fault in an elastic half-space, we find that the rupture occurred on a reverse fault dipping 42¿S, with its upper edge 6 km offshore and lower edge 4 km inland. The amplitude distribution of the coseismic displacements indicates that the rupture did not reach the surface, at least in its western part, and ended to the west around 3.4¿E. Offshore faults like that of the Boumerdes earthquake could account for part of the Africa-Eurasia relative plate motion in the western Mediterranean and represent a significant seismic threat for Algeria.