This paper focuses on low-complexity detection for large scale multiple-input multiple-output (MIMO) systems involving tens to hundreds of transmit/receive antennas. Due to the exponential increase of its processing complexity with the data signal dimensions (antenna number, modulation order), a maximum likelihood detection is infeasible in practice. To overcome this drawback, authors in [1] proposed a low-complexity detection based on a sparse decomposition of the information vector. It is proved that this decomposition is mainly adpated to underdetermined systems and leads to a significant reduction on the processing complexity. As an extension to the work investigated in [1], we propose in this paper a new decomposition that makes the computation cost less dependent on the modulation alphabet cardinality, thus reducing theoretically the complexity by 50% for 4-QAM and by 72% for 16-QAM compared to the previous detector in [1], while achieving the same error rate performance.