S.V.Chmutov, S.V.Duzhin. An upper bound for the number of Vassiliev knot invariants. We prove that the number of independent Vassiliev knot invariants of order $n$ is less than $(n-1)!$ --- thus strengthening the a priori bound $(2n-1)!!$. The paper starts with a short introduction to Vassiliev's theory, which contains the proof of the 4-term relation for chord diagrams from the 4-term relation for knots, invented by the authors.