Nonstationary fractionally integrated time series may possibly be fractionally cointegrated. We propose a test for the null hypothesis of no cointegration building on static regressions of the levels as a first step. Second, an LM test is applied to the regression residuals. However, the application of the LM test to residuals without further modifications does not allow approximate standard normal inference, which contrasts with the situation with observed series. Therefore, we suggest a simple modification of the LM test correcting for the residual effect and for endogeneity of the cointegration regression. The modified procedure guarantees a limiting standard normal distribution.