In this paper, we study the difference equation {(x = [frac(f f f + f + f + f + h, f f + f f + f f + g + h)] (x, ..., x), n = 1, 2, ...; x, x, ..., x > 0,) where f, f, f, g : (R) → R and h : (R) → [0, + ∞) are all continuous functions. We present a sufficient condition for this difference equation to have a globally asymptotically stable equilibrium c = 1. This condition generalizes some previous results. © 2008 Elsevier Ltd. All rights reserved.