Let $\{X(t),\ t>0\}$ be a continuous Gaussian martingale and let $\mathcal H^*$ be the mean-square linear closure of all the one-dimensional polynomials $\{P_n(X(t)),\ n=\overline{1,\ \infty} t>0\}$. For $Y\in\mathcal H^*$, there is the representation $Y=\int_{0}^{\infty}\Phi(t,X(t))\,dX(t)$, $\|\Phi(t,X(t))\|\in\mathcal L_2(\|dx(t)\|^2)$.