Aims: In the present study we investigate the nature of the magnetic Rayleigh-Taylor instability appearing at a tangential discontinuity in a partially ionised plasma when the effect of magnetic shear is taken into account. Methods: The partially ionised character of the plasma is described by the ambipolar diffusion in the induction equation. The dynamics of the plasma is investigated in a single-fluid approximation. After matching the solutions on both sides of the interface we derive a dispersion equation and calculate the instability increment using analytical methods for particular cases of parameters, and numerical investigation for a wide range of parameters. Results: We calculated the dependence of the instability increment on the perturbation wavenumber. We also calculated the dependence of the maximum instability increment on the shear angle of the magnetic field for various values of the ionisation degree. Conclusions: Our results show that the Rayleigh-Taylor instability becomes sensitive to the degree of plasma ionisation only for plasmas with small values of plasma beta and in a very weakly ionised state. Perturbations are unstable only for those wavenumbers that are below a cut-off value.