Let $n\ge 1$, let $M\subset\mathbb C^{n+1}$ be a $C^\infty$ strictly pseudoconvex real hypersurface, and let $p\in M$. Then there exist a neighbourhood $U_0\subset\mathbb C^{n+1}$ of $p$, a neighbourhood $V_0\subset\mathbb C^{n+1}$ of $0$, and a biholomorphic coordinate map $\Psi:U_0\to V_0$ with $\Psi(p)=0$ whose target coordinates are $(z',w)=(z_1,\dots,z_n,w)\in\mathbb C^n\times\mathbb C$. Writing $w=u+iv$ with $u,v\in\mathbb R$, the hypersurface germ $\Psi(M\cap U_0)$ is defined near $0$ by an equation $v=|z'|^2+R(z',u)$, where $R$ is a $C^\infty$ real-valued function defined near $0\in\mathbb C^n\times\mathbb R$ and satisfies $R(z',u)=O\left(|z'|^3+|u||z'|+u^2\right)$ as $(z',u)\to 0$. Equivalently, the remainder has weighted order at least $3$ for the weights $\operatorname{wt}(z_j)=1$ and $\operatorname{wt}(u)=2$. In these coordinates, the leading CR model at $p$ is the Heisenberg quadric $v=|z'|^2$.