One of the main limitations of current remote eye gaze tracking (REGT) techniques is that the user?s head must remain within a very limited area in front of the monitor screen. In this paper we present a free head motion REGT technique. By projecting a known rectangular pattern of lights, the technique estimates the gaze position relative to this rectangle using an invariant property of projective geometry. We carry extensive analysis of similar methods using an eye model to compare their accuracy. Based on these results, we propose a new estimation procedure that compensates the angular difference between the eye visual axis and optical axis. We have developed a real time (30 fps) prototype using a single camera and 5 light sources to generate the light pattern. Experimental results shows that the accuracy of the system is about 1o of visual angle.