Structures of radio galaxies have the potential to reveal inconstancy in the axis of the beams, which reflect the stability in the spin axis of the supermassive black hole at the centre. We present radio observations of the giant radio galaxy B0707-359 whose structure offers an interesting case study of an active galactic nucleus (AGN) that may be exhibiting not only inconstancy in AGN output but also inconstancy in direction of ejection axis. Its radio morphology shows evidence for a restarting of the jets accompanied by an axis change. The observed side-to-side asymmetries of this giant radio galaxy suggest that the new jets are not in the plane of the sky. We infer that the hotspot advance velocities are unusually large and of magnitude a few tenths of the speed of light. The dual-frequency radio images are consistent with a model where the beams from the central engine ceased, creating a relic double radio source; this interruption was accompanied by triggering of a movement of the axis of the central engine at a rate of a few degrees Myr-1. The closer location of the giant radio galaxy axis to the host minor axis rather than the host major axis is supportive of the restarting and axis-change model for the formation of the double-double structure rather than the backflow model. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.