The cointegration tests of Engle and Granger (1987) test the null hypothesis of no cointegration. We extend the unit root testing framework of Kwiatkowski et al (1992) to testing the null hypothesis of cointegration. A test is developed which is asymptotically equivalent to the locally best invariant.(LBI) test and is applicable to a wide range of non-stationary data generating processes. The asymptotic distribution of our test statistic is found to be free of nuisance parameters, and is dependent only on the number of regressors in the cointegrating regression. We tabulate asymptotic critical values for the test based on this distribution, and report on a small power comparison with the Dickey-Fuller test.