For the isolating of nanocrystals from a lignocellulose- or chitin-containing starting material, the starting material is exposed to an oxidative effect of periodate anions in an aqueous suspension. The pH value of the aqueous suspension is adjusted to greater than pH 7.0. The periodate anions are provided in a quantity of at least 5 mol per kg of the starting material, and the starting material is exposed to the oxidative effect of the periodate anions in the aqueous suspension for a period of at least one day.