Equilibrium dialysis measurements show that tRNAfMet1 in 0.17 M Na+ has one strong Mg2+ binding site, K = 3 X 10(4) M-1, and approximately 26 weak binding sites with K = 4 X 10(2) M-1, with RNA concentration measured in moles of tRNA per liter and T = 4 degrees C. The data fit significantly less well to a model with two strong sites and a large class of weak sites. Binding is noncooperative. Our results differ from previous experiments showing cooperative binding because the binding equilibrium is not coupled to a cooperative conformational change of the macromolecule. Measurements at relatively high Na+ concentrations and low temperature ensure that the tRNA is in the "native" region of the conformational phase diagram for all Mg2+ concentrations.