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The usual methods of multiturn injection result in substantial loss which is not acceptable with a high-Power beam. A method first proposed in 1973  is here improved and applied to both the injection of protons and charge-exchange injection. Changes with respect to the original method avoid tunes close to an integer resonance and provide for the necessary tune shift through space-charge forces and nonlinearities in either the pulsed equilibrium-orbit-bump magnets or in fixed octupole magnets. When applied to charge-exchange injection, the method drastically reduces heating and damage to the stripper while providing systematically for the dilution of transverse phase space that is necessary for the intended application--that of injection of 660 turns of a 1.1 GeV, 100 mA beam.