This work reports on investigations of parameters of ion streams emitted from a plasma produced with a picosecond laser at the power densities ≥1016 W/cm2. Not many papers dealing with such investigations have been published up to now, in spite of the fact that the application of precise corpuscular diagnostics enables better learning of the physical properties of such a plasma. As a result of the investigations carried out, the average and maximum energies of Cu ions were 30 keV and 150 keV, respectively. The maximum charge of Cu ions was 13+. The dependencies of parameters of ions emitted from the plasma on the laser-pulse energy as well as on the location of the focus of the laser beam with respect to the target's surface were also found out. The results obtained from the ion measurements in relation to the results of measurements of X ray are discussed.