  Recently, Majorana fermions (MFs) have attracted intensive attention because
of their possible non-Abelian statistics. This paper points out an approach to
verify the non-Abelian statistics of MFs in topological superconductors. We
introduce a single particle representation of braiding operators that obey
anti-commutating relation of Bogolubov-de Gennes (BdG) states. From the
relationship between the braiding operator of MFs and that of BdG states, we
verify non-Abelian statistics of MFs in 1D and 2D topological SCs.
