This paper describes a non-intrusive real-time gaze detection system, characterized by a precise determination of a subject's pupil centre. A narrow field-of-view camera (NFV), focused on one of the subject's eyes follows the head movements in order to keep the pupil centred in the image. When a tracking error is observed, feedback provided by a second camera, in this case a wide field-of-view (WFV) camera, allows quick recovery of the tracking process. Illumination is provided by four infrared LED blocks synchronised with the electronic shutter of the eye camera. The characteristic shape of corneal glints produced by these illuminators allows optimizing the image processing algorithms for gaze detection developed for this system. The illumination power used in this system has been limited to well below maximum recommended levels. After an initial calibration procedure, the line of gaze is determined starting from the vector defined by the pupil centre and a valid glint. The glints are validated using the iris outline to avoid glint distortion produced by changes in the curvature on the ocular globe. In order to minimize measurement error in the pupil-glint vector, algorithms are proposed to determine the pupil centre at sub-pixel resolution. Although the paper describes a desk-mounted prototype, the final implementation is to be installed on board of a conventional car as an embedded system to determine the line of gaze of the driver.