The study shows that a regression model with certain types of disturbances can lead to a false break in the relationship. This false break can happen when using integrated variables in the model. However, if two integrated processes are cointegrated with a structural change, the break point can be accurately estimated. This accuracy is achieved at a fast rate for integrated variables compared to stationary ones. Even small breaks that do not decrease too quickly can be consistently estimated. This finding also applies to models with a broken trend.