Protein-nucleic acids binding driven by electrostatic interactions typically are characterized by the release of counter ions, and the salt-inhibited binding association constant (Ka) and the magnitude of exothermic binding enthalpy (ΔH). Here, we report a non-classical thermodynamics of streptavidin (SA)-aptamer binding in NaCl (140-350 mM) solutions near room temperatures (23-27 °C). By using isothermal titration calorimetry (ITC) and circular dichroism (CD)/fluorescence spectroscopy, we found that the binding was enthalpy driven with a large entropy cost (ΔH -20.58 kcal mol-1, TΔS -10.99 kcal mol-1, and K a 1.08 × 107 M-1 at 140 mM NaCl 25 °C). With the raise of salt concentrations, the ΔH became more exothermic, yet the Ka was almost unchanged (ΔH -26.29 kcal mol-1 and Ka 1.50 × 107 M-1 at 350 mM NaCl 25 °C). The data suggest that no counter Na+ was released in the binding. Spectroscopy data suggest that the binding, with a stoichiometry of 2, was accompanied with substantial conformational changes on SA, and the changes were insensitive to the variation of salt concentrations. To account for the non-classical results, we propose a salt bridge exchange model. The intramolecular binding-site salt bridge(s) of the free SA and the charged phosphate group of aptamers re-organize to form the binding complex by forming a new intermolecular salt bridge(s). The salt bridge exchange binding process requires minimum amount of counter ions releasing but dehydration of the contacting surface of SA and the aptamer. The energy required for dehydration is reduced in the case of binding solution with higher salt concentration and account for the higher binding exothermic mainly.