  $^{235}$U nuclear spin-lattice ($T_1^{-1}$) and spin-spin ($T_2^{-1}$)
relaxation rates in the itinerant antiferromagnet USb$_2$ are reported as a
function of temperature in zero field. The heating effect from the intense rf
pulses that are necessary for the $^{235}$U NMR results in unusual complex
thermal recovery of the nuclear magnetization which does not allow measuring
$T_1^{-1}$ directly. By implementing an indirect method, however, we
successfully extracted $T_1^{-1}$ of the $^{235}$U. We find that the
temperature dependence of $T_1^{-1}$ for both $^{235}$U and $^{121}$Sb follows
the power law ($\propto T^n$) with the small exponent $n=0.3$ suggesting that
the same relaxation mechanism dominates the on-site and the ligand nuclei, but
an anomaly at 5 K was observed, possibly due to the change in the transferred
hyperfine coupling on the Sb site.
