  Dirac Hamiltonian is scaled in the atomic units $\hbar =m=1$, which allows us
to take the non-relativistic limit by setting the Compton wavelength $% \lambda
\rightarrow 0 $. The evolutions of the spin and pseudospin symmetries towards
the non-relativistic limit are investigated by solving the Dirac equation with
the parameter $\lambda$. With $\lambda$ transformation from the original
Compton wavelength to 0, the spin splittings decrease monotonously in all spin
doublets, and the pseudospin splittings increase in several pseudospin
doublets, no change, or even reduce in several other pseudospin doublets. The
various energy splitting behaviors of both the spin and pseudospin doublets
with $\lambda$ are well explained by the perturbation calculations of Dirac
Hamiltonian in the present units. It indicates that the origin of spin symmetry
is entirely due to the relativistic effect, while the origin of pseudospin
symmetry cannot be uniquely attributed to the relativistic effect.
