In this paper, the accuracy of feature points in images detected by the scale invariant feature transform (SIFT) is analyzed. It is shown that there is a systematic error in the feature point localization. The systematic error is caused by the improper subpel and subscale estimation, an interpolation with a parabolic function. To avoid the systematic error, the detection of high-accurate localized features (HALF) is proposed. We present two models for the localization of a feature point in the scale-space, a Gaussian and a Difference of Gaussians based model function. For evaluation, ground truth image data is synthesized to experimentally prove the systematic error of SIFT and to show that the error is eliminated using HALF. Experiments with natural image data show that the proposed methods increase the accuracy of the feature point positions by 13.9% using the Gaussian and by 15.6% using the Difference of Gaussians model.