The paper describes a new phenomenon discovered in the electrolytic analog of a semiconductor diode. As an example, the phenomenon is studied in the 0.1M KOH-0.1M HCl diode where the alkaline and the acidic reservoirs are connected by a hydrogel cylinder. First the traditional, so-called positive salt effect is discussed. In that case some salt is added to the alkaline reservoir of a reverse biased electrolyte diode and as a result, close to a critical concentration of the added salt the electric current increases sharply. The so-called negative salt effect appears as a suppression of the positive one. It is shown by numerical simulations, by approximate analytical formulae, and also by experiments that the high current caused by the salt contamination in the alkaline reservoir can be mostly suppressed by relatively small salt concentrations in the acidic reservoir. Thus a straightforward application of the negative salt effect would be the sensitive detection of nonhydrogen cations in an acidic medium (e.g., in ion chromatography).