The invention relates to a method for displacing a moving plate (20) of a hexapod (100) whose legs (1, 2, 3, 4, 5, 6) are provided with a length adjusting device from an orientation V.sub.i which is defined by the azimuth-elevation coordinates thereof (.alpha..sub.i, .beta..sub.i) towards an orientation V.sub.i+1 which is defined by the azimuth-elevation coordinates thereof (.alpha..sub.i+1, .beta..sub.i+1), characterized in that it comprises stages wherein: a law is defined which defines an offset distance d according to the orientation of the plate (20); the offset distance corresponding to the orientation V.sub.i+1 is determined; the adjustment devices are controlled in order to modify the lengths L.sub.1 L.sub.6 of the legs (1, 2, 3, 4, 5, 6) in order to displace the moving plate (20) from orientation V.sub.1 to orientation V.sub.i+1 and to offset it in relation to the normal on the fixed base (10) of the hexapode (100) via the centre OA of said base (10) on the azimuth plane of V.sub.i+1 of the distance d.