In intensity modulation/direct detection- (IM/DD-) based optical OFDM systems, the requirement of the input signal to be real and positive unipolar imposes a reduction of system performances. Among previously proposed unipolar optical OFDM schemes for optical wireless communications (OWC), asymmetrically clipped optical OFDM (ACO-OFDM) and direct current biased optical OFDM (DCO-OFDM) are the most accepted ones. But those proposed schemes experience either spectral efficiency loss or energy efficiency loss which is a big challenge to realize high speed OWC. To improve the spectral and energy efficiencies, we previously proposed a multistratum-based stratified asymmetrically clipped optical OFDM (STACO-OFDM), and its performance was analyzed for AWGN channel. STACO-OFDM utilizes even subcarriers on the first stratum and odd subcarriers on the rest of strata to transmit multiple ACO-OFDM frames simultaneously. STACO-OFDM provides equal spectral efficiency as DCO-OFDM and better spectral efficiency compared to ACO-OFDM. In this paper, we analyze the BER performance of STACO-OFDM under the effect of multipath fading. The theoretical bit error rate (BER) bound is derived and compared with the simulation results, and good agreement is achieved. Moreover, STACO-OFDM shows better BER performance compared to ACO-OFDM and DCO-OFDM.