Let $X$ be a normal noetherian affine scheme. Let $j:U\rightarrow X$ be a codimension two open of $X$ and $\mathcal{E}$ a vector bundle on $U$.

We assume that $j_*\mathcal{E}$ is a vector bundle. In particular, it is Zariski locally trivial. Can we express a Zariski cover that trivializes $j_{*}\mathcal{E}$ in terms of a Zariski cover that trivializes $\mathcal{E}$?