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In the GCM we study some properties of π meson as the Goldstone bosons in a nuclear matter with finitedensity. Using the effective action in a nuclear matter, we calculate the decay constant and π mass as functions of thechemical potential. The relation between the chemical potential and the density of a nuclear matter is firstly given here.We find that fπ and mπ monotonously decrease as nuclear matter density increases. The result is consistent with theusual assumption that the chiral symmetry is gradually restored as the density of a nuclear matter increases.