In this paper, we investigate the solutions of the higher order difference equation
x_n+1 = \frac{{x_{n - k + 1} }} {{ - 1 + x_n x_n \cdot \cdot \cdot x_{n - k + 1} }} for n = 0,1,...
where k \in {1,2,...} and x_{-k+1}, ..., x_0 are the real numbers such that x_{-k+1}...x_0 \ne 1.