In the current paper we focus on parallelization of non-dominated sorting which is an essential step in Pareto-based multi-objective evolutionary algorithms. The parallel approaches can help to reduce the overall execution time of multi-objective evolutionary algorithms. Although there have been some proposals to parallelize non-dominated sorting algorithms, most of them have focused on the fast non-dominated sort algorithm proposed by Deb et al. This paper explores the scope of parallelism in a recently proposed approach known as Best Order Sort, which was proposed by Roy et al. We focus on two different ways of achieving parallelism in Best Order Sort. The time and space complexity of these two parallel schemes is also analyzed theoretically considering the PRAM CREW model.