Let E; F be vector lattices. We say that a multilinear operatorformulais an orthosymmetric multilinear operator if T(x1; :::; xn) = 0 for all x1; x2; :::; xn 2 E such that jxij ^ jxj j = 0 for some pair of indices 1 · i; j · n. Theorem. n-th order adjoint of an orthosymmetric multilinear mapping on n-th product of a vector lattice is an orthosymmetric multilinear mapping. In this talk, we present n-th order adjoint of a multilinear mapping on product of vector lattices and by using this construction we prove the theorem.