Let $\Omega$ be an open set of $\mathbf{R}^{n}$ and $X \subset \Omega$ a real, coherent analytic set. Suppose that $f : \Omega \to \mathbf{R}$ be a $C^{\infty}$ function such that $f_{|_{x}}$ is analytic. In this paper we want to prove that $f$ may be approached (in sense of Whitney’s theorem) by analytic functions $f_{n} : \Omega \to \mathbf{R}$ such that $f_{n|_{x}} = f_{|_{x}}$