Understanding the phase relationship between climate changes in the Arctic and Antarctic regions is essential for our understanding of the dynamics of the Earth's climate system. In this paper we show that the 20th century de-trended Arctic and Antarctic temperatures vary in anti-phase seesaw pattern – when the Arctic warms the Antarctica cools and visa versa. This is the first time that a bi-polar seesaw pattern has been identified in the 20th century Arctic and Antarctic temperature records. The Arctic (Antarctic) de-trended temperatures are highly correlated (anti-correlated) with the Atlantic Multi-decadal Oscillation (AMO) index suggesting the Atlantic Ocean as a possible link between the climate variability of the Arctic and Antarctic regions. Recent accelerated warming of the Arctic results from a positive reinforcement of the linear warming trend (due to an increasing concentration of greenhouse gases and other possible forcings) by the warming phase of the multidecadal climate variability (due to fluctuations of the Atlantic Ocean circulation).