A novel description of protein structure in terms of the generalized secondary structure elements (GSSE) is proposed. GSSE's are defined as fragments of the protein structure where the chain doesn't radically change its direction. In this new language, global protein topology becomes a particular arrangement of the relatively small number of large, rod like GSSE's. Protein topology can be described by an adjacency matrix giving information, which GSSE's are close in space to each other and defining a graph, where GSSE's are equivalent to vertices and interactions between them to edges. The information about the local structure is translated into the local density of pseudo-Calpha atoms along the chain and the curvature of the chain. This new description has a number of interesting and useful features. For instance, enumeration theorems of graph theory can be used to estimate a number of possible topologies for a protein built from a given number of elements. Different topologies, including novel ones, can be generated from the known by various permutations of elements. Many new regularities in protein structures become suddenly visible in a new description. A new local structure description is more amenable to predictions and easier to use in fold predictions.