A \(k\)-transitive tiling \((k\) being a positive integer) with respect to a crystallographic space group \(G\) of Euclidean space is a tiling whose tiles can be distributed into \(k\) classes so that \(G\) acts transitively on each class. The author considers tilings in three-dimensional euclidean space consisting of polyhedral tiles (i.e. finite unions of polytopes) and presents a gluing procedure to obtain a \((k - 1)\)-transitive tiling from a \(k\)-transitive one.