Symmetry-adapted angular momentum basis functions have been generated for the D-5h* molecular double point group to obtain the self-consistent Dirac cluster wave function Phi and the Dirac cluster orbitals. Once Phi is obtained, we proceed throughout a relativistic first-order perturbation procedure to calculate the magnetic hyperfine tensors of the Ag-7 cluster. The calculated spin distribution and magnetic hyperfine tensors fully support the ESR assignment made by Weltner et al. of a cluster composed of seven silver atoms with a pentagonal bipyramid structure. The single unpaired electron spin spend 40.3% of its time on each axial silver atom.