The current orthogonal cooperative system (OCS) achieves diversity through the use of relays and the consumption of an additional time slot (TS). To guarantee the orthogonality of the received signal and avoid the mutual interference at the destination, the source has to be mute in the second TS. Consequently, the spectral efficiency (SE) is halved. In this paper, linear constellation precoded orthogonal frequency division multiplexing with index modulation (LCP-OFDM-IM) based OCS is proposed, where the source activates the complementary subcarriers to convey the symbols over two TSs. Hence the source can consecutively transmit information to the destination without the mutual interference. Compared with the current OFDM based OCS, the LCP-OFDM-IM based OCS can achieve a higher SE, since the subcarrier activation patterns (SAPs) can be exploited to convey additional information. Furthermore, the optimal precoder, in the sense of maximizing the minimum Euclidean distance of the symbols conveyed on each subcarrier over two TSs, is provided. Simulation results show the superiority of the LCP-OFDM-IM based OCS over the current OFDM based OCS.