Let $\varphi\colon X_{1}\to X_{2}$ be a morphism of proper algebraic varieties over $K$ and ${\overline{L}}_{2}$ a line bundle on $X_{2}$ equipped with an algebraic metric. Assume that $X_{1}$ admits a proper model. Then $\varphi^{*}{\overline{L}}_{2}$, the inverse image under $\varphi$ of ${\overline{L}}_{2}$, is a line bundle on $X_{1}$ equipped with an algebraic metric.