A new beam injection scheme is proposed for the Fermilab Booster to increase beam brightness. The beam is injected on the deceleration part of the sinusoidal magnetic ramp and capture is started immediately after the injection. During the entire capture process we impose Pdot=0 in a changing B field. Beam dynamics simulations clearly show that this method is very efficient with no longitudinal beam emittance dilution and no beam loss. As a consequence of preserved emittance, the required RF power on a typical Booster cycle can be reduced by ~30% as compared with the scheme in current operation. Further, we also propose snap bunch rotation at extraction to reduce dP/P of the beam to improve the slip-stacking efficiency in MI/RR.