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In this paper, we propose a novel reconfigurable intelligent surface (RIS)-based modulation scheme, named RIS-aided receive quadrature reflecting modulation (RIS-RQRM), by resorting to the concept of spatial modulation. In RIS-RQRM, the whole RIS is virtually partitioned into two halves to create signals with only in-phase (I-) and quadrature (Q-) components, respectively, and each half forms a beam to a receive antenna whose index carries the bit information. Furthermore, we design a low-complexity and non-coherent detector for RIS-RQRM, which measures the maximum power and polarities of the I- and Q- components of received signals. Approximate bit error rate (BER) expressions are derived for RIS-RQRM over Rician fading channels. Simulation results show that RIS-RQRM outperforms the existing counterparts without I/Q index modulation in terms of BER in the low signal-to-noise ratio region.