The presence of a binary variable in the cointegrated VAR (CVAR) model is most often interpreted as the structural break affecting the data generating process. It is proved in the paper that to enjoy this interpretation the binary variable must appear simultaneously inside and outside the cointegration space. In order to test for the break we advocate to employ the Wald statistic, however, its critical values and the power had to be simulated separately for the possible change of the constant, the trend, and both. The experiments were designed for different sizes of the cointegrating space, number of variables, the span of the break, normally and t-distributed errors. It is shown that the power of the test depends mostly on the magnitude of the break and the sample size while other factors are of secondary importance. In order to test for the break at unknown period the supWald statistic was proposed.