  By solving the two-body Schordinger equation in a very high precise
nonperturbative numerical (NPnum) way, we reexamine the contributions of fine,
hyperfine structure splittings of muonic hydrogen based on the Breit potential.
The comparison of our results with those by the first order perturbative theory
($^{1st}$PT) in the literature shows, when the structure of proton is
considered, the differences between the results by the $^{1st}$PT and NPnum
methods are small for the fine and hyperfine splitting of $2P$ state, while are
about $-0.009$ meV and $0.08$ meV for the $F=1$ and total hyperfine splitting
of $2S$ state of muonic hydrogen, respectively. These differences are larger
than the current experimental precision and would be significant to be
considered in the theoretical calculation.
