This work is an extension of the research carried out by Jimenez et al. [1] entitled "Start-up electroosmotic flow of Maxwell fluids in a rectangular microchannel with high zeta potentials". They conducted a semi-analytical study of an electroosmotic flow (EOF) with a Maxwell fluid in a rectangular microchannel considering high and asymmetric zeta potentials at the walls of the microchannel. In their solution of the EOF, the separation-of-variables method is used, and derived from the transient-state solution they determined that the limit values of the dimensionless relaxation time are (lambda) over bar (1) = 0 for Newtonian fluids, while for Maxwell fluids values greater than (lambda) over bar (1) > 1/8 pi(2) correspond to square microchannels and (lambda) over bar (1) H*W-2*(2) [4 pi(2) (H*(2) + W*(2))](-1) to rectangular microchannels. This extension provides a general solution for all values of X1 and shows results for 0 <= (lambda) over bar (1) <= H*W-2*(2)[4 pi(2) (H*(2) + W*(2))](-1) that in the above work were not presented. (C) 2016 Elsevier B.V. All rights reserved.