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The filled skutterudite compound CeOs₄Sb₁₂ displays Kondo insulating behavior with accompanied by a ~1 K antiferromagnetic (AFM)/ Spin-Density-Wave (SDW) order state. In penetration depth and magnetic susceptibility measurements, we found a Fermi-surface reconstruction in CeOs₄Sb₁₂ and an unusual phase boundary in the temperature T vs magnetic field H diagram associated with the valence transition from the Ce⁴⁺ to Ce³⁺ state. However, the phase boundary between 5 and 15 K, currently described by the susceptibility data, is hard to define. Since a valence transition can strongly influence the electron-phonon coupling, we performed additional magnetostriction measurements to clarify this intriguing phase boundary.