We show that a Fell bundle B = {B-t}(t is an element of F), over an arbitra
ry free group F, is amenable, whenever it is orthogonal (in the sense that
B-x* x B-y = 0, if x and y are distinct generators of F) and semi-saturated
(in the sense that B-ts coincides with the closed linear span of BtBs, whe
n the multiplication "ts" involves no cancelation).