  Following a previous paper [Haozhao Liang \textit{et al.}, Phys. Rev. C
\textbf{87}, 014334 (2013)], we discuss the spin-orbit effects on the
pseudospin symmetry (PSS) within the framework of supersymmetric quantum
mechanics. By using the perturbation theory, we demonstrate that the
perturbative nature of PSS maintains when a substantial spin-orbit potential is
included. With the explicit PSS-breaking potential, the spin-orbit effects on
the pseudospin-orbit splittings are investigated in a quantitative way.
