In this work, using a combination of experimental design (ED) and artificial neural networks (ANN), the composition of a triethanolamine-buffered chromate electrolyte was optimised for determination of sulphate anions in the presence of high chloride excess. The optimal electrolyte, allowing a baseline-resolved separation of sulphate from chloride present in a 1500 multiple excess in less than 170 s, consists of 10 mmol/L CrO3, 2 mmol/L hexamethonium hydroxide, 10% methanol, and triethanolamine added to adjust the pH to 8.0. The method is suitable to a wide concentration range of chloride (4-1757 mg/L) and sulphate (4-590 mg/L) with linear calibration plots (R-2 = 0.9937-0.9999). Relative standard deviations are less than 2.0% for both anions for migration times and peak areas. The detection limits (hydrodynamic injection of 1 s) were 0.6 mg/L for sulphate and 0.5 mg/L for chloride. The method was successfully applied to determination of sulphate in mineral waters containing a high chloride concentration and to determination of sulphate traces in an anticancer drug injection preparation containing a physiological level of chloride. It was shown that alpha-cyclodextrin as an electrolyte additive has a significant potential for further increasing the separation selectivity for inorganic anions.