  Let $f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x]$, where $a\in\Bbb F_{q^2}^*$. We
prove that $f$ is a permutation polynomial of $\Bbb F_{q^2}$ if and only if one
of the following occurs: (i) $q=2^e$, $e$ odd, and $a^{\frac{q+1}3}$ is a
primitive $3$rd root of unity. (ii) $(q,a)$ belongs to a finite set which is
determined in the paper.
