Recently, it has been debated if the Arctic Oscillation (AO) is a physical oscillation or if it appears as a difference between two regimes. Indications for the latter view include the peaks found in the probability density function in the space spanned by the two leading Empirical Orthogonal Functions (EOFs) of the Northern Hemisphere wintertime 500 hPa heights, and the statistical dependence of these modes. We show that only one of the three reported peaks is statistically significant. Furthermore, an orthonormal rotation suggested by the form of the probability density function itself removes both the statistical dependence and the peaks. The rotated EOFs resemble the patterns of the Pacific/North-American Oscillation and the AO, respectively. The rotation also simplifies the description of the connection to the stratosphere. The phase of the second rotated EOF (the AO) depends strongly on the sign of the stratospheric zonal mean zonal wind 30 days before.