In this paper there is proved a generalization of the results of Whitehead and Pontryagin on the homotopy classification of closed, simply connected four-manifolds. Let W and M be compact four-dimensional simply connected oriented four-manifolds. By q_w is denoted the intersection index on the group H₂(W). Basic Result. THEOREM (Extension). Let the groups H₁(δW)and H₁(δM) be finite and suppose given a homotopy equivalence f:δW→δM. In order that f can be extended to a homotopy equivalence (W,δW)→(M,δM), it is necessary and sufficient that there should exist an isomorphism Ξ, such that the diagram[Figure not available: see fulltext.] is commutative and Ξ*q_m=q_m.