Homotopy classification of PD4-complexes relative an order relation

We define an order relation among oriented PD4$$\textit{PD}_4$$-complexes. We show that with respect to this relation, two PD4$$\textit{PD}_4$$-complexes over the same complex are homotopy equivalent if and only if there is an isometry between the second homology groups. We also consider minimal objects of this relation.