When the probe function f(r) is chosen to be f(r)=r, the statistical correlation coefficient tau[f] reduces to the angular correlation coefficient tau[r], which provides an overall measure of the difference between the electron-pair density and the product of single-electron densities. For a pair of atomic Hartree-Fock spin-orbitals i and j, the characteristics of the angular correlation coefficient tau(ij)[r] are studied. The coefficient tau(ij)[r] is found to be negative for two spin-orbitals with the same spin and with azimuthal quantum numbers different by unity and zero for other cases. It is shown that tau(ij)[r] is expressible in terms of the generalized electron-pair moments [q(2)]((a,b))(ij) relevant to the spin-orbitals i and j. Especially, the relation for a=b=1 means that tau(ij)[r] is nothing but the difference between the center-of-mass motion and relative motion contributions of two electrons in those spin-orbitals. A numerical examination of 102 neutral atoms shows that the angular correlation is generally largest between the outermost s and p subshells.