Three-dimensional structures of proteins are the support of their biological functions. Their folds are maintained by inter-residue interactions which are one of the main focuses to understand the mechanisms of protein folding and stability. Furthermore, protein structures can be composed of single or multiple functional domains that can fold and function independently. Hence, dividing a protein into domains is useful for obtaining an accurate structure and function determination. In previous studies, we enlightened protein contact properties according to different definitions and developed a novel methodology named Protein Peeling. Within protein structures, Protein Peeling characterizes small successive compact units along the sequence called protein units (PUs). The cutting done by Protein Peeling maximizes the number of contacts within the PUs and minimizes the number of contacts between them. This method is so a relevant tool in the context of the protein folding research and particularly regarding the hierarchical model proposed by George Rose. Here, we accurately analyze the PUs at different levels of cutting, using a non-redundant protein databank. Distribution of PU sizes, number of PUs or their accessibility are screened to determine their common and different features. Moreover, we highlight the preferential amino acid interactions inside and between PUs. Our results show that PUs are clearly an intermediate level between secondary structures and protein structural domains.