In this note, we consider global asymptotic stability of the following nonlinear difference equation x n = ( ∏ i = 1 v ( x n - k i β i + 1 ) + ∏ i = 1 v ( x n - k i β i - 1 ) ) / ( ∏ i = 1 v ( x n - k i β i + 1 ) - ∏ i = 1 v ( x n - k i β i - 1 ) ) , n = 0,1 , … , where k i ∈ ℕ ( i = 1,2 , … , v ) , v ≥ 2 , β 1 ∈ [ - 1,1 ] , β 2 , β 3 , … , β v ∈ ( - ∞ , + ∞ ) , x - m , x - m + 1 , … , x - 1 ∈ ( 0 , ∞ ) , and m = max 1 ≤ i ≤ v { k i } . Our result generalizes the corresponding results in the recent literature and simultaneously conforms to a conjecture in the work by Berenhaut et al. (2007).