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Most available remote eye gaze trackers based on pupil center corneal reflection (PCCR) technique have two characteristics that prevent them from being widely used as an important computer input device for human computer interaction. First, they must often be calibrated repeatedly for each individual; second, they have low tolerance for head movements and require the user to hold the head uncomfortably still. In this paper, we propose a solution for the classical PCCR technique that simplify the calibration procedure and allow free head movements. The core of our method is to analytically obtain a head mapping function to compensate head movement. Specifically, the head mapping function allows to automatically map the eye movement measurement under an arbitrary head position to a reference head position so that the gaze can be estimated from the mapped eye measurement with respect to the reference head position. Furthermore, our method minimizes the calibration procedure to only one time for each individual. Our proposed method significantly improves the usability of the eye gaze tracking technology, which is a major step for eye tracker to be accepted as a natural computer input device.