According to the recent suggestion by M. Rudolph [J. Electroanal. Chem. 529 (2002) 97], the point method of the finite-difference electrochemical simulations suffers from a considerable loss of accuracy, when used in conjunction with moderately or strongly non-uniform exponentially expanding spatial grids defined by coordinate transformation. Furthermore, Rudolph concludes that when using a three-point approximation for the second spatial derivative, the point method cannot be better than first-order accurate in such cases. These opinions are debatable because they have been confirmed by the examination of only two variants of the point method. We investigate an alternative variant of the point method, also based on a three-point discretisation of the second spatial derivative on the uniform grid of the transformed space coordinate. This discretisation contradicts the Rudolph opinions because it is second-order accurate and it provides distinctly more accurate results than the variants considered by Rudolph. This is demonstrated for the example of the simulation of the potential step chronoamperometry under limiting current conditions at a planar electrode. (C) 2003 Elsevier B.V. All rights reserved.