Group testing enables the identification of a small subset of defective items within a larger population by performing tests on pools of items rather than on each item individually. Over the years, it has not only attracted attention from the academic community, but has also demonstrated its potential in addressing real-world problems such as infectious disease screening, drug discovery and manufacturing quality control. With the emergence of the COVID-19 pandemic, interest in group testing has grown further, particularly in non-adaptive testing, due to its time efficiency compared to adaptive approaches. This highlights the importance of improving the performance currently achievable in such a scheme. This article focuses on advancing the field of noiseless non-adaptive group testing. The main objective of this work is to study and maximize the probability of successfully identifying the subset of defective items while performing as few tests as possible. To this end, we first note current well-known decoding algorithms, as well as established test design strategies for assigning items to pools. From this review, we identify key opportunities for improvement that inform the development of new decoding algorithms. Specifically, we propose a novel method, Weighted Sequential Combinatorial Orthogonal Matching Pursuit (W-SCOMP), to enhance the efficiency of existing detection procedures. Theoretical results demonstrate that W-SCOMP outperforms other algorithms in noiseless non-adaptive group testing. Furthermore, we develop a simulation framework to model the group testing process and conduct comparative evaluations between the proposed and existing algorithms. The empirical results are consistent with the theoretical findings. Overall, our work expands the range of available decoding algorithms and contributes to the broader understanding of noiseless non-adaptive group testing.