Summary: In this paper, the authors solve the difference equation \[ x_{n+1} =\frac{x_nx_{n-2}}{-ax_n + bx_{n-2}}, \quad n = 0, 1, \dots, \] where \(a\) and \(b\) are positive real numbers and the initial values \(x_{-2}, x_{-1}\) and \(x_0\) are real numbers. The authors find invariant sets and discuss the global behavior of the solutions of that equation. It is shown that when \(a > \frac{4}{27}b^3\), under certain conditions there exist solutions, either periodic or converge to periodic solutions.