this a joint work with wanke yin. let $m\subset \mathbb{c}^{n+1}$ ($n\ge 2$) be a real analytic submanifold defined by an equation of the form: $w=|z|^2+o(|z|^3)$, where we use $(z,w)\in {cc}^{n}\times cc$ for the coordinates of ${c}^{n+1}$. we first derive a pseudo-normal form for $m$ near $0$. we then use it to prove that $(m,0)$ is holomorphically equivalent to the quadric $(m_\infty: w=|z|^2,\ 0)$ if and only if it can be formally transformed to $(m_\infty,0)$, using the rapid convergence method. we also use it to give a necessary and sufficient condition when $(m,0)$ can be formally flattened. our main theorem generalizes a classical result of moser for the case of $n=1$.