Reflection modulation based on reconfigurable intelligent surface (RIS) is considered to be a promising information transfer mechanism without requiring any additional radio frequency chains. However, existing reflection modulation schemes consider manipulating the ON/OFF states of RIS elements, which suffers from power loss. In this paper, we propose a new scheme, called RIS-aided quadrature reflection modulation (RIS-QRM), for harvesting the reflection power based on an RIS-aided downlink multiple-input single-output (MISO) wireless system. To this end, RIS-QRM partitions RIS elements into two subsets for reflecting impinging signals into two orthogonal directions as well as passive beamforming and encodes its local data onto the element partition options. A closed-form expression for the unconditional pairwise error probability of RIS-QRM in Rician fading is derived assuming the maximum-likelihood detection. Moreover, we propose a low-complexity detection method with compromised performance for decoupling the joint search of the constellation symbol and the RIS element partition. Computer simulation results corroborate the effectiveness of RIS-QRM and validate the analytical results. It is shown that RIS-QRM is able to improve the error performance of the additional bits delivered by the RIS without deteriorating that of the bits carried on the constellation symbol, as compared to ON/OFF-based schemes.