  We have performed a precision atomic interferometry experiment on testing the
universality of free fall (UFF) considering atoms' spin degree of freedom. Our
experiment employs the Bragg atom interferometer with $^{87}$Rb atoms either in
hyperfine state $\left| {F = 1,{m_F} = 0} \right\rangle $ or $\left| {F =
2,{m_F} = 0} \right\rangle $, and the wave packets in these two states are
diffracted in one pair of Bragg beams alternatively, which can help suppress
the common-mode systematic errors. We have obtained an
E$\rm{\ddot{o}}$tv$\rm{\ddot{o}}$s ratio $\eta = \left( { 0.9 \pm 2.7} \right)
\times {10^{ - 10}}$, and set a new record on the precision with a nearly 5
times improvement. Our experiment gives stronger restrictions on the possible
UFF breaking mechanism.
