An {\it ornament} is a finite collection of closed oriented curves in the plane, none three of which have common intersection. Homotopy invariants of ornaments are considered in this paper. Like for classification of knots, all invariants of ornaments are equal to the linking numbers with appropriate cycles in the {\it discriminant\/}, i.e. in the set of collections of curves with forbidden intersections. Finite order (or Vassiliev) invariants are those for which this cycle can be described in terms of finitely many strata of natural stratification of the discriminant by the types of forbidden points. Calculation of these invariants is reduced to calculation of certain cohomological spectral sequences. A new explicit combinatorial construction of series of finite order invariants of ornaments is given in the paper. It is shown that some of previously known series of finite order invariants are covered by this series and can also be represented as cohomology classes in natural finite-dimensional topological spaces.