Orthogonal Frequency Division Multiplexing (OFDM) with Index Modulation (OFDM-IM), which conveyed information bits via the activated indices and constellation symbols is a promising technique in the next wireless communications. In the OFDM-IM scheme, only part of subcarriers are activated to transmit information, the inactive subcarriers transmit zero symbols, so that the conventional differential coding is not suitable for the adjacent subcarriers. In order to address this issue, in this paper, a novel Rectangular Differential OFDM-IM (RD-OFDM-IM) scheme is proposed to exploit the benefits of OFDM-IM dispensing with Channel State Information (CSI). In the proposed RD-OFDM-IM scheme, N subcarriers are partitioned into G subblocks and index modulation is employed in each subblock first. Then rectangular differential coding is invoked during two adjacent subblocks, so that nocoherent detection can be employed for the proposed RD-OFDM-IM scheme. Simulation results are shown that the proposed RD-OFDM-IM scheme is capable of providing considerable performance gain over conventional Differential OFDM (D-OFDM) scheme with lower Peak Average Power Ratio (PAPR).