Reversible logic has been considered as an important solution to the power dissipation problem in the existing electronic devices. Many universal reversible libraries that include more than one type of gates have been proposed in the literature. This paper proposes a novel reversible n-bit gate that is proved to be universal for synthesizing reversible circuits. Reducing the reversible circuit synthesis problem to permutation group allows Schreier-Sims Algorithm for the strong generating set-finding problem to be used in the synthesize of reversible circuits using the proposed gate. A novel optimization rules will be proposed to further optimize the synthesized circuits in terms of the number of gates, the quantum cost and the utilization of library to achieve better results than that shown in the literature.