[en] This paper presents the results of an experiment in which the polarization parameter P in π⁺ p elastic scattering has been measured in the energy range from 335 to 580 MeV. The experiment was performed on a pion channel of the LNPI syncro-cyclotron using a polarized proton target and wire spark chambers with magnetostrictive read-out. The results have substantially higher precision in comparison with the most of other experiments in this energy range and allow to determine unambiguously the shape of angular dependence P(thetasup(*)) in the whole investigated region. New phase-shift analysis of π⁺p scattering data has been performed. The results of this experiment were used also to check isospin invariance. (orig.)