This paper presents evidence of a non-linear relationship between real GDP growth and oil price changes for the US economy. We also argue that this non-linearity is not merely due to the use of data from the mid-1980s onwards, as most authors, so far, seem to believe. In fact, we find the existence of non-linearity with the use of data earlier than 1984, and even before 1977 Furthermore, we question that the non-linear transformations of oil prices proposed in the literature are the most appropriate ones for reflecting such non-linearity.