This paper studies the global asymptotic stability for positive solutions to the higher order rational difference equation x n = ( ∏ j = 1 m ( x n − k j + 1 ) + ∏ j = 1 m ( x n − k j − 1 ) ) / ( ∏ j = 1 m ( x n − k j + 1 ) − ∏ j = 1 m ( x n − k j − 1 ) ) ,   n = 0 , 1 , 2 , … , where m is odd and x − k m , x − k m + 1 , … , x − 1 ∈ ( 0 , ∞ ) . Our main result generalizes several others in the recent literature and confirms a conjecture by Berenhaut et al., 2007.