$N$ is determined by $\n$, the CR distributions of $N$ are precisely the CR distributions of $\n$.

\[D1\] A CR distribution $u$ on $\n$ is decomposable at the point $Z\in \n$ if, near $Z$, $u=\sum_{j=1}^KU_j$ where the $U_j$ are CR distributions extending holomorphically to wedges $\W_j$ in $\C^{k+m}$ with edges $\n$. We shall say a CR distribution $u$ on $N$ is decomposable at a point $p=(p',h(p'))$ if $u$ is decomposable at $p'$ on $\n$.

\[t1\] Let $N=\{(\n,h(\n))\} $ be a smooth ($\CC^{\infty})$ non generic CR submanifold of $\C^{k+m+n}$ such that the function $h$ decomposable at some $p'_0 \in \n$. Let $v$ be a complex transversal vector to $N$ at $p_0=(p'_0,h(p'_0))$.

[**(A)**]{} If $f$ is a decomposable CR distribution at $p_0$, then, near $p_0$, there exists a wedge $\W$ of direction $v$ whose edge contains a neighborhood of $p_0$ in $N$ and $F\in \O(\W)$ such that the boundary value of $F$ on $N$ is $f$.

[**(B)**]{} There exists a wedge $\W$ of direction $v$ and $\{F_{\l}\}_{\l=1}^n$, $F_{\l}\in
\O(\W)$ such that $dF_1\wedge ...\wedge dF_n\not = 0$ on $\W$ and each $F_{\l}$ vanishes to order one on $N$.

We also get as a corollary:

\[t3\] Let $M$ be a smooth ($\CC^{\infty}$) generic submanifold 