This paper presents the transmission performance of a class-IV partial-response signaling SSB system and proposes a method that can improve its power efficiency. A line code that has no dc component has been used in the SSB transmission of digital signals. The type of line code, such as a partial-response signaling, increases the modulation states, and as a result, decreases the power efficiency. To overcome this obstacle, a new demodulation method called "re-filtering and combining" is proposed on the assumption of orthogonal phase detection. The demodulated quadrature channel is re-filtered by a Hilbert filter and is combined with the in-phase channel. It is confirmed by computer simulations that the new demodulation method improves the BER performance and a 3 dB improvement of the power efficiency is obtained.