This paper is concerned with the oscillation of second order linear functional equations of the form x(g(t)) = P(t)x(t) + Q(t)x(g2(t)), where P, Q,g: [t0, ∞) → R+ =[0, ∞) are given real valued functions such that g(t) t, limt-∞g(t) = ∞. It is proved here that when 0 ≤ m := lim inft-∞ Q(t)P(g(t)) ≤ 1/4 all solutions of this equation oscillate if the condition limn sup Q(t)P(g(t)) ＞is satisfied. It should be emphasized that the condition (*) can not be improved in some sense.