Previous empirical studies have suggested an ambiguous relationship between crude oil prices and exchange rates. In contrast with these studies, we explore the possibility of a non-linear relationship between oil prices and the Norwegian exchange rate. We reveal a negative relationship between oil prices and the value of the Norwegian exchange rate that is relatively strong when oil prices are below 14 dollars and are falling. Allowance for this non-linear relationship leads to an econometrically well specified and interpretable exchange rate model that also has strong predictive properties. Notably, this model substantially improves the forecasts compared with those from a similar model but with linear oil price effects and a random walk model. We undertake an extensive evaluation of our findings to demonstrate their robustness.