Let X be a complete algebraic variety over a field F. We show that the functor taking a cycle module M over F to the group of unramified elements in M(F(X)) is represented by a cycle module. It is shown that every unramified element in M(F(X)) for all M is constant if and only if the degree map CH0(XL) → Z is an isomorphism for every field extension L/F. Functorial properties of the unramified elements will be discussed.