In this article we have tried to critically analyze the factors which cause the condensed Fukui function (FF) indices [f(r)] to attain a negative value in some cases. The evaluation of condensed FF indices needs finite-difference approximation to the electronic charge densities, and the finite-difference approximation needs partitioning of the electronic charge to the constituent atoms. In a previous article [J. Chem. Phys. 110, 8236 (1999)] we have argued that the probable factors, which cause the FF indices to appear negative in some cases, may be (i) the improper charge partitioning techniques adopted to evaluate f(r); (ii) large change in the electron number (Delta N = 1) when f(r) is evaluated in condensed form using the finite-difference approximation. In this article we want to focus more on the first factor. The present study shows through pictorial as well as numerical demonstrations of the charge-density difference [rho(neutral)((r) over bar)-rho(cation)((r) over bar) and rho(anion)((r) over bar)-rho(neutral)((r) over bar)] plots, how the negative condensed FF value appears with the use of improper charge partitioning and how the use of Hirshfeld partitioning can solve this problem.