  We present the explicit forms of the maximum eigenvalue and the corresponding
eigenfunction for the second-order reduced density matrix (RDM2) of the BCS
superconducting state (SS). Using these quantities, we deal with two topics in
the present paper. As the first topic, it is shown that the cluster
decomposition principle holds in the BCS-SS. This proof gives a theoretical
foundation that the abnormal density can be chosen as the order parameter of
the SS. As the second topic, it is shown that such an eigenfunction is spin
singlet and spatially extends isotopically, and further that the mean distance
of two electrons which consists of the above eigenfunction is in a good
agreement with Pippard's coherence length. This means that maximum geminal of
the RDM2 of the BCS-SS can be regarded as the Cooper pair itself which are
condensed to the same energy level in a number of O(N).
