In a recent work, we have shown that the plasma flow around the magnetic island can excite the beta-induced Alfvén eigenmode (BAE) (Marchenko et al 2016 Nucl. Fusion56 106021). In the present communication, it is shown that coupling of this primary BAE and magnetic island generates secondary geodesic acoustic mode (GAM), which has the frequency and mode structure identical to those of the primary BAE. The fixed GAM/BAE amplitude ratio, determined by the plasma neutrality, is comparable with the plasma/magnetic pressure ratio. This nonlinear coupling can be responsible for axis-symmetric modes, which accompany island-driven Alfvénic modes observed on HL-2A tokamak (Chen et al 2013 Nucl. Fusion53 113010).