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The time series of the euro/dollar exchange rate can be analyzed correctly by incorporating a discontinuity in the form of a “thick transitory break”. If we examine the period from the Louvre agreements to March 2009 but eliminate the euro’s initial years, we can conclude that the rate is level-stationary or trend-stationary, and thus that a self-correcting mechanism returns the rate to an equilibrium level (or trend). We demonstrate this effect using a new test procedure based on the elimination of “thick transitory breaks”. More generally, we confirm the assumption that, thanks to the existence of deterministic trends with breaks, exchange-rate variations can be explained without necessarily referring to fundamentals.