  Prescribed rational functions constitute a subset of rational functions
satisfying certain symmetry and analyticity conditions. We define and construct
explicitly prescribed rational functions-valued bundle $\mathcal{W}_M$ over a
smooth complex curve $M$. An intrinsic coordinate-independent formulation for
such bundle is is given. The construction presented in this paper is useful for
studies of the canonical cosimplicial cohomology of infinite-dimensional Lie
algebras on smooth manifolds, as well as for purposed of conformal field
theory, deformation theory, and the theory of foliations.
