In the recent publications (Gerace and Savona, Phys. Rev. A 89(R), 031803 2014; Zhou et al., Opt. Express 24, 17332 2016), the unconventional photon blockades are studied in a three-mode-second-order-nonlinearity system with linear coupling between the two low frequency modes. In this paper, the unconventional photon blockade is studied in a complementary case with linear coupling between the two high frequency modes. By solving the master equation in the steady-state limit and calculating the zerodelay- time second-order correlation function, a strong photon antibunching is found in this three-mode-second-order-nonlinearity system. The optimal antibunching conditions are derived and the numerical simulations confirm the optimal conditions. Our scheme can be used as a tunable single-photon source.