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Let (X,Y) be a random vector with joint probability measure σ and with margins μ and ν. Let ${\left(Pₙ\right)}_{n\in \mathbb{N}}$ and ${\left(Qₙ\right)}_{n\in \mathbb{N}}$ be two bases of complete orthonormal polynomials with respect to μ and ν, respectively. Under integrability conditions we have the following polynomial expansion: $\sigma (dx,dy)={\sum }_{n,k\in \mathbb{N}}{\varrho }_{n,k}Pₙ\left(x\right)Q_k\left(y\right)\mu \left(dx\right)\nu \left(dy\right)$. In this paper we consider the problem of changing the margin μ into μ̃ in this expansion. That is the case when μ is the true (or estimated) margin and μ̃ is its approximation. It is shown that a new joint probability with new margins...