EN
We clarify how the natural transformations of fiber product preserving bundle functors on $ℱ ℳ_m$ can be constructed by using reductions of the rth order frame bundle of the base, $ℱ ℳ_m$ being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.