We propose and demonstrate a simple and novel technique to accelerate the carrier injection/depletion processes in an RSOA by applying instantaneous injection/depletion currents at the transition edges of the modulation signal to force the carrier density to respond at a high speed and, as a result, to increase its modulation speed. We theoretically and experimentally show that, by using the proposed technique, it is possible to obtain 5 Gbit/s optical BPSK signal from an RSOA having a modulation bandwidth of only 0.9 GHz.