As already noticed in other telescopes, the presence of large telescope spiders and of a segmented deformable mirror in an Adaptive Optics system leads to pupil fragmentation and may create phase discontinuities. On the ELT telescope, a typical effect is the differential piston, where all disconnected areas of the pupil create their own piston, unseen locally but drastically degrading the final image quality. The poor sensitivity of the Pyramid WFS to differential piston will lead to these modes been badly seen and therefore badly controlled by the adaptive optics (AO) loop. In close loop operation, differential pistons between segments will start to appear and settle around integer values of the average sensing wavelength. These additional differential pistons are artificially injected by the adaptive optics control loop but do not have any real physical origin, contrary to the Low Wind Effect. In an attempt to reduce the impact of unwanted differential pistons that are injected by the AO loop, we propose a novel approach based on the pair-wise coupling of the actuators sitting on the edges of the deformable mirror segments. In this paper, we present the correction principle, its performance in nominal seeing condition, and its robustness relative to changing seeing conditions, wind speed and natural guide star magnitude. We show that the edge actuator coupling is a simple and robust solution and that the additional quadratic error relative to the reference case (i.e. no spiders) is of only 40 nm RMS, well within the requirements for HARMONI.