Index Modulation Multiple Access (IMMA) technique is proposed recently as a viable candidate for future wireless networks. The idea is to utilize the available orthogonal resources for multiple users as index constellation symbols and allow users to access all available resources without any need of scheduling algorithm. Yet, IMMA receiver applies brute-force search algorithm and suffers from immense computational complexity. Also, IMMA applies index modulation and allows each user to activate a single orthogonal resource at each transmission time. Hence, this letter aims at enhancing the overall performance of IMMA by allowing each user to activate two of the available orthogonal resources to transmit orthogonal data. As well, a novel low complexity receiver is proposed and shown to significantly reduce the computational complexity without any performance degradation. The new scheme is called Quadrature IMMMA (QIMMA) and shown to have superior performance, in terms of number of users and error probability, as compared to IMMA scheme. Analytical framework to compute the average bit error probability for the proposed QIMMA is derived and substantiated through Monte Carlo simulation results.