Abstract: The concept of orthogonal design of experiments is generalized and some new ideas are proposed in this paper. Let us consider the model Y=η(X)+εwhere Y can be observed and ε is the random error. One always makes assumption that η（X） is the linear combination of known function φ_i（X）, i=1, …, p, for classical expe- rimental design. But now, η（X） is assumed to be a function defined on R^m. We consider X as a random vector taking value in R^m. Any distribution of X is called a design, and if its components are independent of each other, then it is called orthogonal. Let X_a=(x_i2, x_i2, …, x_iα) with 1≤i₁≤i₂…＜i_α≤m, 1≤α≤m, and \mu\left(X_a\right)=\sum_\beta=0^\infty(-1)^a-\beta \sum_X_a \subset X_\theta M\left(X_\beta\right) where M （X_β）=E （η（X）/X_β） then μ（X_α） is called interactive effective function among x_i1, x_i2…, x_iα. In this paper, we give the decomposition \eta(X)=\sum_\beta=0^m \sum_X_A \subset X \mu\left(X_B\right) and discuss the properties of effective function for generalized orthogonal experimental designs. Finally, some numerical examples are given.