In a recent paper, Caserta et al. [M. Caserta, S. Schwarze, and S. Vob\A mathematical formulation and complexity considerations for the blocks relocation problem", European Journal of Operational Research, 219, pp.96-104 (2012)] proposed two mathematical models for the blocks relocation problem. Because of the complexity of their first model, called BRP-I, they employed a simplifying assumption and introduced a relatively fast model, called BRP-II, to solve medium-sized instances. In this paper, it is first proven that the BRP-II model is incorrect. Then, the corrected and improved formulation of BRP-II, called BRP2c and BRP2ci, respectively, are presented. By correcting a constraint in BRP-II, the reported optimal solution is either corrected or improved in many instances. Also, it is proven that some results of BRP-II reported by Caserta et al. are incorrect. Incorporating some new cut constraints into BRP2ci, the computational time of solving instances is decreased 25 times, on average.