The rigidity theorem for homotopy invariant presheaves with Witt-transfers on the category of smooth schemes over a field k of characteristic different form two is proved. Namely, for any such sheaf F, isomorphism F(U) F(x) is established, where U is an essentially smooth local Henselian scheme with a separable residue field over k. As a consequence, the rigidity theorem for the presheaves Wⁱ(-xY) for any smooth Y over k is obtained, where the Wⁱ(-) are derived Witt groups. Note that the result of the work is rigidity with integral coefficients. Other known results are state isomorphisms with finite coefficients.