An EOF analysis of a constructed time series mimicking the Northern Hemisphere SLP variability of the last 50 years shows that the Barents Oscillation (BO) appears as a means to represent the sudden eastward shift of the northern center of action associated with the Arctic Oscillation (AO) observed in the mid-seventies. This sudden shift (non-stationarity) appears in an EOF analysis as a step change in the relative phase between the principal components associated with the EOFs of the AO and BO. The results also show that an EOF analysis of a constant amplitude signal can produce artificial trends and/or amplitude changes in the principal component associated with a given mode (eg. AO) when such non-stationarities are present in the signal. In this case, different modes of variability represented by EOF's cannot be considered independently from one another. In the example presented, although the principal components are completely uncorrelated from one another, perfect correlation and anti-correlation are present in the first and second parts of the time series respectively.