Research of visual cognition often suffers from very inexact methods of eye movement recording. A so-called eye tracker, fastened to the test person's head, yields information about pupil position and facing direction related to a computer monitor in front of the subject. It is now a software task to calculate the coordinates of the screen point the person is looking at. Conventional algorithms are not able to realize the required non-linear projection very precisely. Especially if the test person is wearing spectacles, the deviation may exceed 3 degrees of visual angle. In this paper a new approach is presented, solving the problem with a parametrized self-organizing map (PSOM). After a short calibration it reduces the average error to approximately 30 percent of its initial value. Due to its high efficiency (less than 150 μs per computation on a PC with a 486DX2-66 processor) it is perfectly suited for real-time application.