The analysis of previously reported shortcomings of the condensed Fukui functions obtained making use of the quantum theory of atoms in molecules indicates these drawbacks are due to the inadequacy of the definition employed to compute them and not to the partitioning. A new procedure, which respects the mathematical definition and solves these problems, is presented for the calculation of condensed Fukui functions for atomic basins defined according to the quantum theory of atoms in molecules. It is tested in a set of 18molecules, which includes the most controversial reported cases.