By employing the self-modulation birefringence difference in a semiconductor optical amplifier (SOA), an improved method is proposed to generate a complete optical single-sideband (OSSB) signal. Over $30\mathrm{dB}$ sideband suppression ratios (SSRs) of lower OSSB signals are obtained over a $12\mathrm{dB}$ input power range and a $36\mathrm{nm}$ wavelength span, with a maximum of over $35\mathrm{dB}$ . Upper OSSB signals with an SSR of over $15\mathrm{dB}$ are observed using a SOA for what is believed to be the first time. This method is effective even for the carrier-suppressed signal. The theory for OSSB generation in an SOA is extended and verified by experiment.