It is well accepted that increasing atmospheric CO<sub>2</sub> results in global warming, leading to a decline in polar sea ice area. Here, the specific question of whether there is a tipping point in the sea ice cover is investigated. The global climate model HadCM3, is used to map the trajectory of sea ice area under idealised scenarios. The atmospheric CO<sub>2</sub> is first ramped up to four times pre-industrial levels (4 × CO<sub>2</sub>) then ramped down back to pre-industrial levels. We also examine the impact of stabilising climate at 4 × CO<sub>2</sub> prior to ramping CO<sub>2</sub> down to pre-industrial levels. Against global mean temperature Arctic sea ice area has little hysteresis while the Antarctic sea ice shows significant hysteresis – its rate of change slower, with falling temperatures, than its rate of change with rising temperatures. However, we show that the driver of the hysteresis is the hemispherical differences in temperature change between transient and stabilisation periods. We find no irreversible behaviour in the sea ice cover.