We reformulate the concept of connection on a Hopf-Galois extension B ⊆ P in order to apply it in computing the Chern-Connes pairing between the cyclic cohomology HC 2n (B) and K 0 (B). This reformulation allows us to show that a Hopf-Galois extension admitting a strong connection is projective and left faithfully flat. It also enables us to conclude that a strong connection is a Cuntz-Quillen-type bimodule connection. To exemplify the theory, we construct a strong connection (super Dirac monopole) to find out the Chern-Connes pairing for the super line bundles associated to super Hopf fibration.