The aim of the presented research was to obtain reconstituted atelocollagen fibers after extraction from poultry cartilage using the pepsin-acidic method in order to remove telopeptides from the tropocollagen. Firstly, we examined the extraction of collagen from the cartilage extracellular matrix (ECM) after proteoglycans (PG) had been removed by the action of salts, i.e., NaCl or chaotropic MgCl2. Additionally, the effects of the salt type used for PG and hyaluronic acid removal on the properties of self-assembled fibers in solutions at pH 7.4 and freeze-dried matrices were investigated. The basic features of the obtained fibers were characterized, including thermal properties using scanning calorimetry, rheological properties using dynamic oscillatory rheometry, and the structure by scanning electron microscopy. The fibers obtained after PG removal with both analyzed types of salts had similar thermal denaturation characteristics. However, the fibers after PG removal with NaCl, in contrast to those obtained after MgCl2 treatment, showed different rheological properties during gelatinization and smaller diameter size. Moreover, the degree of fibrillogenesis of collagens after NaCl treatment was complete compared to that with MgCl2, which was only partial (70%). The structures of fibers after lyophilization were fundamentally different. The matrices obtained after NaCl pretreatment form regular scaffolds in contrast to the thin, surface structures of the cartilage matrix after proteoglycans removal using MgCl2.