The majority of planetary aurorae are produced by electrical currents flowing between the ionosphere and the magnetosphere which accelerate energetic charged particles that hit the upper atmosphere. At Saturn, these processes collisionally excite hydrogen, causing ultraviolet emission, and ionize the hydrogen, leading to H3+ infrared emission. Although the morphology of these aurorae is affected by changes in the solar wind, the source of the currents which produce them is a matter of debate. Recent models predict only weak emission away from the main auroral oval. Here we report images that show emission both poleward and equatorward of the main oval (separated by a region of low emission). The extensive polar emission is highly variable with time, and disappears when the main oval has a spiral morphology; this suggests that although the polar emission may be associated with minor increases in the dynamic pressure from the solar wind, it is not directly linked to strong magnetospheric compressions. This aurora appears to be unique to Saturn and cannot be explained using our current understanding of Saturn's magnetosphere. The equatorward arc of emission exists only on the nightside of the planet, and arises from internal magnetospheric processes that are currently unknown.