  Within a transport model, we study the neutron-proton differential transverse
flow and its excitation function in central $^{132}$Sn + $^{124}$Sn collisions
at 270 MeV/nucleon. To more accurately evaluate effects of the high-density
behavior of symmetry energy \esym on this observable, we also consider the
uncertainties of \esym around the saturation density $\rho_{0}$. It is shown
that the neutron-proton differential transverse flow and its excitation
function are mainly sensitive to the slope $L$ of \esym at $\rho_{0}$. However,
the effects of low-density behavior of \esym on this observable should also be
considered. Therefore, it is suggested that measurements of the neutron-proton
differential transverse flow and its excitation function may provide useful
complements to the constraints on $L$ extracted from the spectral pion ratio in
S$\pi$RIT experiments.
