Structural relaxation in a magnetic metallic glass having composition ${\mathrm{Fe}}_{78}$${\mathrm{Si}}_{9}$${\mathrm{B}}_{13}$ has been studied using Mo\ifmmode\ddot\else\textasciidieresis\fi{}ssbauer spectroscopy. Information about the atomic-level changes occurring in the specimen has been obtained through the correlated distributions of the hyperfine-interaction parameters. Increasing annealing temperature causes a decrease in the geometrical distortions as well as a change in topological short-range order. These changes involve (i) a decrease in the average interatomic spacing, and (ii) topological rearrangement of atoms resulting in significant changes in the population of transition-metal sites with different numbers of metalloid near neighbors.