The paper proposes a method for identifying fingerprints that is resistant to noise and image defects. The method relies on minutiae, bifurcations and endings, which, under the influence of defects, can change their type. Such undesirable changes affect the ridge counting, the topological and other characteristics of the images. It can reduce the reliability of their identification. To compensate for the effect of interference, a topological vector is introduced and its numbering rules for bifurcations and endings are described. A method is proposed for converting topological vectors from one type of minutiae to another. As a result of the cast, topological vectors for bifurcations and endings are numbered alike. This ensures the stability of the ridge counting, the reliability of matching of various topological vectors and, consequently, the minimal identification errors. The method is implemented in the algorithm. The results of testing the proposed method are given.