[en] The present conception of LAMPF II is a high-intensity 16-GeV synchrotron injected by the LAMPF 800-MeV H^- beam. The proton beam will be used to make secondary beams of neutrinos, muons, pions, kaons, antiprotons, and hyperons more intense than those of any existing or proposed accelerator. For example, by taking maximum advantage of a thick target, modern beam optics, and the LAMPF II proton beam, it will be possible to make a negative muon beam with nearly 100% duty factor and nearly 100 times the flux of the existing Stopped Muon Channel (SMC). Because the unique features of the proposed machine are most applicable to beams of the same momentum as LAMPF (that is, < 2 GeV/c), it may be possible to use most of the experimental areas and some of the auxiliary equipment, including spectrometers, with the new accelerator. The complete facility will provide improved technology for many areas of physics already available at LAMPF and will allow expansion of medium-energy physics to include kaons, antiprotons, and hyperons. When LAMPF II comes on line in 1990 LAMPF will have been operational for 18 years and a major upgrade such as this proposal will be reasonable and prudent