Abstract—This note discusses a particular kind of ternary functional decomposition based on a ternary function ↑ to be performed on the set of composite functions. Such function is closely related to the cycling concept of Postian algebras. A systematic method is given to determine the set of all decompositions of that kind admitted by the function. Such set is called the cyclo-set and it is proved that it is a filter in the partitions lattice. Since any partition of the lattice can be expressed as an intersection of cardinality-2 partitions, it follows that the method consists merely in finding the infimum of the cardinality-2 partitions belonging to the cyclo-set and then determining the filter having this infimum as vertex. The existence of proper subsets of the cardinality-2 partitions set leading to the determination of the ifiter-vertex is discussed, and results obtained for functions of domain-order up to seven are stated. Finally, the total number of cyclo-decompositions for a given partitional structure is calculated.