This correspondence proposes the use of a real-only equalizer (ROE), which acts on real signals derived from the received offset quadrature amplitude modulation (OQAM) symbols. For the same fading channel, we prove that both ROE and the widely linear equalizer (WLE) yield equivalent outputs. Hence, these exhibit the same performance. Our complexity analysis finds that depending on the frame length, ROE can be computationally less complex, and save significant signal processing time over WLE. In the adaptive normalized least mean square implementation, ROE performs better with lower complexity than its counterpart, for a given number of pilot bits.