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Electrooculography (EOG) is one of the measures used to estimate the direction of a person's gaze; however, conventional EOG techniques suffer from a drift issue which makes it difficult to extract an accurate absolute eye angle. The technique proposed here is based on the nonlinearity of the EOG and offers a practical solution to this problem. It estimates the absolute eye angles before and after a saccade, which cancels the offset due to the drift. Additionally, it does not require any effort from the user or any target, but instead uses only the difference of the EOGs. Experiments with five subjects confirm that the proposed technique can estimate the absolute eye angle with an error of less than 4(°). They also show improvements are achieved with several options such as weighting and multiple saccades. The technique will contribute to practical EOG-based interaction systems.