Let k be an infinite field and B = k[X1,…, Xn] a polynomial ring over k. Let M be a finitely generated module over B. For every prime ideal P ⊂ B let μ(MP) be the minimum number of generators of Mp, i.e., μ(MP) = dimBP/PP(MP®BP (BP/PP)). Set η(M) = max(μ(MP) + dim(B/P)|P ∄ SpecB such that MP is not free). Then M can be generated by η(M) elements. This improves earlier results of A. Sathaye and N. Mohan Kumar on a conjecture of Eisenbud-Evans.