The polarization of the secondary protons in the (p, 2p) reaction with the S-shell protons of nuclei 4 He, 6 Li, 12 C, 28 Si, 40 Ca was measured at 1 GeV unpolarized proton beam. The spin correlation parameters C ij for the 4 He and 12 C targets also were for the first time obtained as well. The polarization measurements were performed by means of a two-arm magnetic spectrometer, each arm of which was equipped with the multiwire-proportional chamber polarimeter. This experiment was aimed to study a modification of the proton-proton scattering matrix in the nuclear medium. Comments: 28 pages, 7 figures, 6 tables, Submitted to the journal "Physics of Atomic Nuclei" Category: Nuclear experiment (nucl-ex)