A ternary relation C on a set G is called a cyclic order iff it is asymmetric, i.e. (x,y,z)\(\in C\Rightarrow (z,y,x)\not\in C\), transitive, i.e. (x,y,z)\(\in C\), (x,z,u)\(\in C\Rightarrow (x,y,u)\in C\), and cyclic, i.e. (x,y,z)\(\in C\Rightarrow (y,z,x)\in C\). The authors define and study the operation \(P_{\omega}(G,H)\) (G and H are cyclically ordered sets) which has the following property of the power of ordered sets: if G is nondiscrete and H contains no isolated elements, then \(P_{\omega}(G,H)\) is antiisomorphic with H.