Professor Trinajstic´ devoted years of research to deepen the knowledge of the distance-based topological indices. He was especially interested in so-called Szeged-type indices. Several such indices were introduced directly by himself, but none of them was named after him. In this paper, a novel topological invariant of this kind is proposed, and it is boldly named the Trinajstic´ index. The performed computational tests are justifying the introduction of this novel topological index.