  We construct a hyperbolic modular double -- an algebra lying in between the
Faddeev modular double for $U_q(sl_2)$ and the elliptic modular double. The
intertwining operator for this algebra leads to an integral operator solution
of the Yang-Baxter equation associated with a generalized Faddeev-Volkov
lattice model introduced by the second author. We describe also the L-operator
and finite-dimensional R-matrices for this model.
