The atom-bond connectivity index is a recently introduced topological index defined as [Formula: see text], where du denotes degree of vertex u. Here we define a new version of the ABC index as [Formula: see text], where nu denotes the number of vertices of G whose distances to vertex u are smaller than those to other vertex v of the edge e = uv, and nv is defined analogously. The goal of this paper is to study the ABC2 index.