The present invention is a method of separating nucleic acid molecules from contaminants, such as proteins, in a solution and isolating one or more desired nucleic acid molecules, which method comprises the following steps (a) providing an aqueous adsorption solution, which includes nucleic acids and a salt that forms lyotropic ions when dissolved; (b) passing said solution over a matrix to adsorb the nucleic acids onto the matrix, said matrix including an aromatic ring moiety and at least one thioether moiety; (c) passing an aqueous eluent over said matrix to desorb the nucleic acid molecules therefrom, which eluent includes a salt that forms lyotropic ions and a gradient of increasing ionic strength originating from an increasing concentration of a salt that forms less lyotropic ions when dissolved than the ones present in said aqueous adsorption solution; and (d) isolating a fraction comprising the desired nucleic acid molecules.