Interresidue protein contacts in proteins structures and at protein-protein interface are classically described by the amino acid types of interacting residues and the local structural context of the contact, if any, is described using secondary structures. In this study, we present an alternate analysis of interresidue contact using local structures defined by the structural alphabet introduced by Camproux et al. This structural alphabet allows to describe a 3D structure as a sequence of prototype fragments called structural letters, of 27 different types. Each residue can then be assigned to a particular local structure, even in loop regions. The analysis of interresidue contacts within protein structures defined using Voronoï tessellations reveals that pairwise contact specificity is greater in terms of structural letters than amino acids. Using a simple heuristic based on specificity score comparison, we find that 74% of the long-range contacts within protein structures are better described using structural letters than amino acid types. The investigation is extended to a set of protein-protein complexes, showing that the similar global rules apply as for intraprotein contacts, with 64% of the interprotein contacts best described by local structures. We then present an evaluation of pairing functions integrating structural letters to decoy scoring and show that some complexes could benefit from the use of structural letter-based pairing functions.