  We consider the max-type equation
$$x_{n+4}=\max\{x_{n+3},x_{n+2},x_{n+1},0\}-x_n,$$ with arbitrary real initial
conditions. We describe completely its set of periods $\mathrm{Per}(F_4)$, as
well as its associate periodic orbits. We also prove that there exists a
natural number $N\notin\mathrm{Per}(F_4)$ for which $$\left\{N+m:m\geq
1,m\in\mathbb N\right\}\subset\mathrm{Per}(F_4).$$
