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The mass matrix for $\eta-\eta^\prime$ is derived in the flavor basis at${\cal O}(p^4)$ of the chiral Lagrangian using the large $N$ approximation.Under certain assumptions, the mixing angle $\phi=41.4^\circ$ and the decayconstants ratio $f_K/f_\pi=1.15$ are calculated in agreement with the data. Itappears that the FKS scheme arises as a special limit of the chiral Lagrangian.Their mass matrix is obtained without the hypothesis on the mixing pattern ofthe decay constants.

$\eta-\eta^\prime$ Mixing in the Flavor Basis and Large N