Matching feature points between images is one of the most fundamental issues in computer vision tasks. As the number of feature points increases, the feature matching rapidly becomes a bottleneck. In this paper, a novel method is presented to accelerate features matching by two modifications of the popular SIFT algorithm. The first modification is based on splitting the SIFT features into two types, Maxima- and Minima-SIFT features, and making comparisons only between the features of the same type, which reduces the matching time to 50% with respect to the original SIFT. In the second modification, the SIFT feature is extended by a new attribute which is an angle between two independent orientations. Based on this angle, SIFT features are divided into subsets and only the features with the difference of their angles less than a pre-set threshold value are compared. The performance of the proposed methods was tested on two groups of images, real-world stereo images and standard dataset ...