In this paper, a novel spectrum sharing scheme, based on orthogonal frequency division multiplexing with index modulation (OFDM-IM), is proposed for cognitive radio networks. In the considered model, the primary transmitter communicates with the primary receiver with the aid of an amplify-and-forward (AF) relay by transmitting OFDM-IM signals. Meanwhile, the secondary transmitter passively senses the spectrum and transmits its own information over those inactive subcarriers of the primary network to the secondary receiver. Through the proposed protocol, inactive subcarriers inherent in the existing OFDM-IM systems can be fully exploited, thus improving the spectral efficiency. To evaluate the performance, closed-form upper bounds on the bit error rate (BER) are derived for both users utilizing the optimal maximum-likelihood detection. Simulation results corroborate the analysis and show that the proposed scheme has the potential of outperforming OFDM-IM-AF in terms of BER with higher spectral efficiency.