We study the integrable nonlinear hyperbolic equation ${u}_{xy} = u{u}_{xx} + \frac{1}{2} u_{x}^{2} + u$, which is a generalization of the Hunter—Saxton equation considered by Manna and Neveu. We show that associated with this equation is a hierarchy of local symmetries $U_i$, $i \in \mathbb{Z}$. We present a recursion operator and its inverse. Remarkably enough both are second order integro-differential operators and reduce the order of symmetries in the half of hierarchy.