When a neutron star forms, after the collapse of its progenitor, a strong magnetic field survives in its interior. This magnetic topology is usually assumed to be well approximated by a dipole located right at the centre of the star. However, there is no particular reason why this dipole should be attached to this very special point. A slight shift from the stellar centre could have strong implications for the surrounding electromagnetic field configuration leading to clear observational signatures. We study the effect of the most general off-centred dipole anchored in the neutron star interior. Exact analytical solutions are given in vacuum outside the star to any order of accuracy in the small parameter = d/R, where d is the displacement of the dipole from the stellar centre and R the neutron star radius. As a simple diagnostic of this decentred dipole, the spin-down luminosity and the torque exerted on its crust are computed to the lowest leading order in. Results are compared to earlier works and a discussion on repercussions on pulsar braking index and multiwavelength light curves is proposed.