Current knowledge about tectonic plate movement is widely applied in numerous scientific fields; however, questions still remain to be answered. In this study, the focus is on the determination and analysis of the parameters that describe tectonic plate movement, i.e., the position (F and L) of the rotation pole and angular rotation speed (w). The study was based on observational material, namely the positions and velocities of the GNSS stations in the International Terrestrial Reference Frame 2014 (ITRF2014), and based on these data, the motion parameters of five major tectonic plates were determined. All calculations were performed using software based on a least squares adjustment procedure that was developed by the author. The following results were obtained: for the African plate, Φ = 49.15 ± 0.10°, Λ = −80.82 ± 0.30°, and ω = 0.267 ± 0.001°/Ma; for the Australian plate, Φ = 32.94 ± 0.05°, Λ = 37.70 ± 0.12°, and ω = 0.624 ± 0.001°/Ma; for the South American plate, Φ = –19.03 ± 0.20°, Λ = −119.78 ± 0.39°, and ω = 0.117 ± 0.001°/Ma; for the Pacific plate, Φ = −62.45 ± 0.07°, Λ = 111.01 ± 0.14°, and ω = 0.667 ± 0.001°/Ma; and for the Antarctic plate, Φ = 61.54 ± 0.30°, Λ = −123.01 ± 0.49°, and ω = 0.241 ± 0.003°/Ma. Then, the results were compared with the geological plate motion model NNR-MORVEL56 and the geodetic model ITRF2014 PMM, with good agreement. In the study, a new approach is proposed for determining plate motion parameters, namely the sequential method. This method allows one to optimize the data by determining the minimum number of stations required for a stable solution and by identifying the stations that negatively affect the quality of the solution and increase the formal errors of the determined parameters. It was found that the stability of the solutions of the F, L, and w parameters varied depending on the parameters and the individual tectonic plates.