Symmetries of a certain periodic chain

We consider a periodic closure of a nonlinear integrable two-dimensional three-point chain. Integrability is understood in the sense that the chain admits a wide class of reductions, which are nonlinear hyperbolic Darboux integrable systems with two independent variables. We consider a system obtained as a period-$2$ periodic closure of one of two-dimensional three-point chains found within this framework. For this system, a second-order higher symmetry depending on two arbitrary functions is constructed.