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The characteristics of electrokinetic flow in a microchannel depend on both the nature of the surface potential, i.e. whether it is uniform or nonuniform, and the electric potential distribution along the channel. In this paper, the nonlinear Poisson-Boltzmann equation is used to model the electrical double layer and the Lattice Boltzmann Model coupled with the constraint of current continuity is used to simulate the flow field in a rectangular microchannel with step change surface potential. The results show that step change ion distribution caused by step change surface potential will influence significantly the electric potential distribution along the channel, the velocity profiles and the volumetric flow rate. This may indicate that if disturbance on the ion distribution due to nonuniform surface potential and velocity distortion is large and not negligible, the electric potential distribution along the channel in both pressure-driven and electroosmotic flow may not be linear.