In this paper, we solve the difference equation,x(n+1) = alpha/1 - x(n)x(n-1), n = 0, 1, ...,,where alpha > 0 and the initial values x(-1), x(0) are real numbers. We find invariant sets and discuss the global behavior of the solutions of that equation. We show that when alpha < 2/3 root 3, one of the positive equilibrium points attracts all orbits with initials outside a set of Lebesgue measure zero. Also, when alpha = 2/3 root 3, the unique positive equilibrium points attracts all orbits with initials outside a set of Lebesgue measure zero. Finally, we show that when alpha > 2/3 root 3, under certain conditions there exist solutions that are either periodic or converging to periodic solutions and give some examples. We show also the existence of dense solutions in the real line.