The music video, featuring both Annie Lennox and Dave Stewart, was directed by Stewart, John Gerschfield and Jon Roseman, and released in December 1983, a month before the single came out. The video opens with a passing aerial shot of The Old Man of Hoy on the Island of Hoy in the Orkney Islands before transitioning to Lennox walking along the rocky shore and cliff top. She later explores a derelict cottage while wearing a nightgown and holding a lantern. Stewart stalks her with a video camera. In many scenes the two are filmed separately, then superimposed into the same frame. The result is that the viewer may perceive one as being a ghost in the world of the other.