A new polarized-proton and -antiproton beam with 185 GeV/c momentum has been built at Fermilab. The design uses the parity-nonconserving decays of lambda and antilambda hyperons to produce polarized protons and antiprotons, respectively, a beam-transport system that minimizes depolarization effects, and a set of twelve dipole magnets that rotate the beam-particle spin direction. A beam-tagging system determines the momentum and polarization of individual beam particles. This allows a selection of particles in definite intervals of momentum and polarization. Measurements performed by two different polarimeters showed that the beam is polarized and the determination of polarization by beam-particle tagging is verified. A new measurement of the analyzing power of large-xF π0 production may lead to another beam polarimeter.