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We construct a formal normal form for a real 2-codimensional submanifold$M\subset\mathbb{C}^{N+1}$ near a CR singularity approximating the sphere. Thisresult gives a higher dimensional extension of Huang-Yin's normal form in$\mathbb{C}^{2}$.

A normal form for a real 2-codimensional submanifold in $\mathbb{C}^{N+1}$ near a CR singularity