In this paper, we demonstrate a performance boost by parallelizing a purely functional bisimulation algorithm on a multicore processor machine. The key idea of this parallelization is exploiting the referential transparency of purely functional programs to minimize refactoring of the original implementation without any parallel constructs. Both original and parallel implementations are written in Haskell, a purely functional programming language. The change from the original program to the parallel program is minuscule, maintaining almost original structure of the program. Through benchmark, we show that the proposed parallelization doubles the performance of the bisimulation test compared to the original non-parallel implementation. We also shaw that similar performance boost is also possible for a memoized version of the bisimulation implementation.