Let (A, m) be a Cohen-Macaulay local ring of dimension d ≥ 1 and I an ideal in A. Let M be a finitely generated maximal Cohen-MacaulayAmodule. Let I be a locally complete intersection ideal with ht M (I) = d − 1, l M (I) = d and reduction number at most one. We prove that the polynomial n → ℓ(Tor A 1 (M, A/I n+1 )) either has degree d − 1 or F I (M ) is a free F (I)−module.