We derive the Barankin bound on the mean-squared error for multiple change-point estimation of an independent measurement sequence. We first derive a general form of this bound and give the structure of the so-called Barankin information matrix (BIM). We show that the BIMfor the change-point parameters has a tri-diagonal structure which means that one change-point estimation depends on its neighboring change points. Using this result, we propose a computationally efficient inversion algorithm of the BIM. As an illustration, we analyze the case of changes in the mean vector of a Gaussian distribution.