The conductivity of sodium poly(styrenesulfonate) solution was found to increase during dialysis against water as indicated by the in-situ conductivity measurements at a concentration of c = 0.1 g/L which is in the dilute/semidilute region. To interpret this unexpected phenomenon, the domains of polyion chains and their aggregates are assumed to have a uniformly charged density. Although the aggregation resulted from the higher attractive forces rather than the repulsion between the polyion chains, their size was determined by the counterbalance of ionic osmotic forces due to the fact that the interior of aggregated domains has more counterions than the exterior. When the polyelectrolyte solution was dialyzed against water, extra osmotic forces acted on the solution due-to Donnan's effects. On the basis of the mean field theory and above arguments, the increase of conductivity during dialysis was interpreted in terms of the aggregation of polyions in the aqueous solution.