The solubility diagram of the quinary system Na+-Mg++-1-aminonaphtalene-6-sulfonate-1-aminonaphtalene-7-sulfonate-Cl–-H2O has been partially investigated between 0° and 75°. From this diagram a simple and effective procedure to separate the two CLEVE'S acids has been calculated, with yields in acid 1.7 (extracted as sodium salt) of 95.1% and in acid 1.6 (obtained as magnesium salt) of 70.0%. This theoretical procedure was adapted to the fractionnation of a crude industrial mixture of CLEVE's acids.