In a face recognition system, the normalization of the faces under scale, rotation and translation, as well as under contrast and brightness variation, is a crucial step for the extraction of stable features used to recognize a face. A way to improve the speed and the recognition performance of the overall system, is to have an accurate normalization of the images, especially in scale. Here, we present an algorithm, which constitutes the fine analysis part of a multi-scale face detection algorithm in a complex background [3], and which detects, with a subpixellic precision, the center and the ray of the eyeballs of a person's eyes. The segment joining these two points is then used to achieve a geometrical normalization of the face's image under scale, rotation and translation. One of the major advantages of this method is to reduce greatly the number of possible scales used during the face recognition process.