This paper proposes a simple direct testing procedure to distinguish a linear unit root process from a globally stationary three-regime self-exciting threshold autoregressive process. Following the threshold cointegration literature and thus assuming that the process follows the random walk in the corridor regime, the null of a unit root can be tested by the Wald test for the joint significance of threshold autoregressive parameters under the lower and the upper regime. We derive the asymptotic null distribution of the Wald statistic, and show that it does not depend on unknown fixed threshold values. Monte Carlo evidence clearly indicates that the exponential average of the Wald statistic is more powerful than the Dickey-Fuller test that ignores the threshold nature under the alternative.