Under this paper’s project, an attempt was made to obtain linear glucans by precipitating them from a solution of potato starch dissolved in DMSO and hydrolyzed by a commercial pullulanase preparation called ‘Pulluzyme 750’ (ABM Chemicals). The precipitation procedure included three steps, after each step completed, a different fraction of hydrolyzate was obtained. The following values were determined in individual fractions obtained: the amylose chains content, the molecular mass distribution, the retrogradation tendency, and the phase transition characteristics using a DSC method. It was stated that the fraction III had the most interesting properties. The fraction III was composed mostly of short-chain amylose and it exhibited the highest tendency to retrograde. A significant enthalpy of the melting of the retrograded fraction III and the high phase transition temperatures prove a high content of amylose crystallites, which appear characteristic of a resistant starch.