Let f=a\x+\x^{3q-2}\in\Bbb F_{q^2}[\x], where aβFq2ββ. We
prove that f is a permutation polynomial of Fq2β if and only if one
of the following occurs: (i) q=2e, e odd, and a3q+1β is a
primitive 3rd root of unity. (ii) (q,a) belongs to a finite set which is
determined in the paper