The deletion of a trend as an initial step in the analysis of climatic time series may result in the elimination of low-frequency components which constitute an integral part of climatic variability. An example is given here showing that linear trend deletion from the time series of the World Ocean annual sea-surface temperature (1850–2009) reduces the low-frequency (from 0.02 year–1 to 0.001 year–1) part of the time series spectrum by ∼40% to 80% thus severely distorting the spectrum of climate. As an additional result, it is shown that the current warming can be explained in full within the framework of a stationary stochastic model fitted directly to the time series of annual sea-surface temperature (SST) from 1850 through 2009 with no trend deletion. According to the model, the recurrence time of runs of generally increasing temperature by ∼0.5°C lasting for several decades (as has been observed since about 1956) is about 500 years for the World Ocean. Thus, the current run of growing SST is not an extremely rare event in climate and can be explained as a part of the natural climatic variability. These results show that deleting linear trends requires a thorough preliminary analysis. It is suggested that the approach described here can be used to improve physical models of the World Ocean climate.