We design a new scheme for the accurate localization of markers in images of calibration plates. This forms the basis of so-called fixed or strong camera calibration methods. We focus on the most widely used plates with circular markers arranged in a regular grid. Our algorithm is fully automatic and very robust. We assess its results by using synthetic images containing noise and other practical image detoriations. Comparing with the ground truth of the marker positions, we obtain a localization precision of 0.01 pixel in high-quality images, and 0.03 pixel in very bad quality images (high noise, low contrast, lens distortion, CCD misplacements). With these results, the algorithm outperforms all existing algorithms from literature.