A wireless communications system with a transmission rate of 10 Mbit/s using Japanese ISM band (2471-2497 MHz) is presented. This system employs a novel spread spectrum multiple access method named "CFO-SS (Carrier Frequency Offset-Spread Spectrum)" method. In the CFO-SS system, a single PN code is commonly assigned to all the multiple carriers, and the frequency offset between the carriers is determined by the information symbol rate, which is small as compared with the spread bandwidth of the signal. Bit error rate performance of the proposed CFO-SS system under multipath environments is investigated by computer simulation, and the performance of the CFO-SS method is confirmed for wireless LAN systems using the 2.4 GHz ISM band.