  Let $k$ be a positive integer and $S_{2k}={\tt x}+{\tt x}^4+...+{\tt
x}^{4^{2k-1}}\in\Bbb F_2[{\tt x}]$. It was recently conjectured that ${\tt
x}+S_{2k}^{4^{2k}}+S_{2k}^{4^k+3}$ is a permutation polynomial of $\Bbb
F_{4^{3k}}$. In this note, the conjecture is confirmed and a generalization is
obtained.
