ABSTRACT We examine the non-linear variability of quasi-periodic oscillations (QPOs) using the bicoherence, a measure of phase coupling at different Fourier frequencies. We analyse several observations of RXTE/PCA archival data of the black hole binary GX 339-4 which show QPOs. In the type C QPOs, we confirm the presence of the ‘hypotenuse’ pattern where there is non-linear coupling between low frequencies that sum to the QPO frequency as well as the ‘web’ pattern, where in addition to the hypotenuse, non-linear coupling between the QPO frequency and the broad-band noise is present. We find that type B QPOs show a previously unknown pattern. We also show that the bicoherence pattern changes gradually from ‘web’ to ‘hypotenuse’ as the source moves from a hard intermediate state to a soft intermediate state. Additionally, we reconstruct the QPO waveforms from six observations using the biphase. Finally, we present a scenario by which a moderate increase in the optical depth of the hard X-ray emission region can explain the changes in the non-linearity seen during this transition.