Index modulation has become a promising technique in the context of orthogonal frequency division multiplexing (OFDM), whereby the specific activation of the frequency domain subcarriers is used for implicitly conveying extra information, hence improving the achievable throughput at a given bit error ratio (BER) performance. In this paper, a dual-mode OFDM technique (DM-OFDM) is proposed, which is combined with index modulation and enhances the attainable throughput of conventional index-modulation-based OFDM. In particular, the subcarriers are divided into several subblocks, and in each subblock, all the subcarriers are partitioned into two groups, modulated by a pair of distinguishable modem-mode constellations, respectively. Hence, the information bits are conveyed not only by the classic constellation symbols, but also implicitly by the specific activated subcarrier indices, representing the subcarriers' constellation mode. At the receiver, a maximum likelihood (ML) detector and a reduced-complexity near optimal log-likelihood ratio-based detector are invoked for demodulation. The minimum distance between the different legitimate realizations of the OFDM subblocks is calculated for characterizing the performance of DM-OFDM. Then, the associated theoretical analysis based on the pairwise error probability is carried out for estimating the BER of DM-OFDM. Furthermore, the simulation results confirm that at a given throughput, DM-OFDM achieves a considerably better BER performance than other OFDM systems using index modulation, while imposing the same or lower computational complexity. The results also demonstrate that the performance of the proposed low-complexity detector is indistinguishable from that of the ML detector, provided that the system's signal to noise ratio is sufficiently high.