In this paper we propose a novel high-performance algorithm, referred to as MARSs (Matrix Algorithm for RNA Secondary Structure Prediction), for predicting RNA Secondary Structures with or without pseudoknots. The algorithm is capable of operating in both serial and parallel modes. The algorithm will take complete advantage of the explicit hardware parallelism increasingly available in todayś multi-core processors resulting in execution speedups. Unlike Dynamic Programming based algorithms, MARSs is non-recursive by design and therefore eliminates some of the disadvantages of Dynamic Programming based algorithms. We performed a large-scale experiment on a multi-core hardware using real sequences with verified structures. We detail and discuss the results from these experiments using metrics such as performance gains, run-times and prediction accuracy. This is one of the first attempts of its kind to provide a complete flexibility in evolving a RNA secondary structure with or without pseudoknots using a matrix-based approach.