Differential　subcarrier　index　modulation　(DSIM)　is　an　emerging　OFDM　with　index　modulation　(OFDM-IM)　technique,　which　does　not　require　channel　state　information　(CSI)　at　the　receiver.　However,　the　DSIM　scheme　has　two　drawbacks　of　lower　spectral　efficiency　and　lacking　transmit　diversity.　In　this　letter,　by　combining　rectangular　differential　coding　and　coordinate　interleaving　orthogonal　design,　a　novel　rectangular　differential　OFDM-IM　using　coordinate　interleaving　(CI-OFDM-RDIM)　scheme　is　proposed.　In　this　scheme,　the　dispersion　matrix　is　projected　to　a　dispersion　vector　that　is　transmitted　in　a　single　symbol　interval,　so　that　CI-OFDM-RDIM　improves　spectral　efficiency　compared　with　DSIM.　Since　the　symbols　in　two　adjacent　differential　groups　are　interleaved,　the　proposed　scheme　obtains　diversity　gain.　Furthermore,　owing　to　the　orthogonality　of　its　processing　matrix,　a　low-complexity　decoupled　maximum　likelihood　(D-ML)　detector　is　proposed.　Theoretical　performance　analysis　and　simulation　results　show　that　CI-OFDM-RDIM　outperforms　DSIM　in　terms　of　the　bit　error　rate　(BER)　performance.　©　1997-2012　IEEE.