Bieri-Eckmann [6] introduced the concept of relative cohomology  for a group pair  where G is a group and  is a family  of subgroups of G and, by using that theory, they introduced the concept of Poincaré duality pairs  and provided a topological interpretation for such pairs through Eilenberg-MacLane pairs  A Poincaré duality pair is a pair  that satisfies  two isomorphisms, one between absolute cohomology and relative homology and the second between relative cohomology and absolute homology. In this paper, we present a proof that those two isomorphisms are equivalent. We also present some calculations on duality pairs by using the cohomological invariant defined in [1] and studied in [2-4].