The polarization parameter in π +p backward elastic scattering at 6 GeV/ c incident pion momentum has been measured using a butanol polarized proton target, a high intensity pion beam, and a scintillation hodoscope detection system. Details of the apparatus and data analysis are presented here, together with the final results. The polarization appears to be very nearly zero for small u-values, but becomes large and negative for u-values beyond the dip in the π +p cross section at u = −0.15(GeV/ c) 2. The data are not well predicted by any of the current Regge-exchange models.