The pixel detector is the most internal detector of the tracking system on the CMS experiment at the LHC. This detector provides the most accurate measurements for a complete reconstruction of traces and vertices of charged particles. The fitting algorithms known as KVF, AVF, TKF and GSF for such a reconstruction have been developed, implemented and studied within the working framework of the CMS. At this moment, KVF, AVF and TKF algorithms have been already validated and adjusted to find the best performance for each one in order to select the optimum fit for primary vertices. In the following research work, I offer the data from the first validation of the GSF algorithm for the H → ZZ → 4e – and H → ZZ → 4mu samples, and analyze the obtained results. This kind of validation is on the frontier of research in this field.