The ITEP-PNPI collaboration presents the results of the measurements of the spin rotation parameter A in the elastic scattering of positive and negative pions on protons at P_beam = 1.62 GeV/c. The setup included a longitudinally-polarized proton target with superconductive magnet, multiwire spark chambers and a carbon polarimeter with thick filter. Results are compared to the predictions of partial wave analyses. The experiment was performed at the ITEP proton synchrotron, Moscow.