Let M be a smooth manifold of dimension m>0, and denote by $S_{can}$ the canonical Nijenhuis tensor on TM. Let Π be a Poisson bivector on M and ${\Pi }^T$ the complete lift of Π on TM. In a previous paper, we have shown that $(TM,{\Pi }^T,S_{can})$ is a Poisson-Nijenhuis manifold. Recently, the higher order tangent lifts of Poisson manifolds from M to $T^{r}M$ have been studied and some properties were given. Furthermore, the canonical Nijenhuis tensors on $T^{A}M$ are described by A. Cabras and I. Kolář [Arch. Math. (Brno) 38 (2002), 243-257],...