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Remote eye-gaze tracking provides a means for nonintrusive tracking of the point-of-gaze (POG) of a user. For application as a user interface for the disabled, a remote system that is noncontact, reliable, and permits head motion is very desirable. The system-calibration-free pupil-corneal reflection (P-CR) vector technique for POG estimation is a popular method due to its simplicity, however, accuracy has been shown to be degraded with head displacement. Model-based POG-estimation methods were developed, which improve system accuracy during head displacement, however, these methods require complex system calibration in addition to user calibration. In this paper, the use of multiple corneal reflections and point-pattern matching allows for a scaling correction of the P-CR vector for head displacements as well as an improvement in system robustness to corneal reflection distortion, leading to improved POG-estimation accuracy. To demonstrate the improvement in performance, the enhanced multiple corneal reflection P-CR method is compared to the monocular and binocular accuracy of the traditional single corneal reflection P-CR method, and a model-based method of POG estimation for various head displacements.