A novel modulation technique coined SIM-OFDM was recently proposed. SIM-OFDM uses different frequency carrier states to convey information and leads to increased performance in comparison to conventional OFDM. Additionally, its innovative structure can lead to a decrease of the peak system power, which is highly beneficial in the context of optical wireless communication. One of the issues of the original SIM-OFDM scheme is a potential bit error propagation which could lead to significant burst errors. The current paper proposes a modified technique which avoids bit error propagation whilst retaining the benefits of the concept.