Let X, Y be cell complexes, let U be an Abelian group, and let f : [X, Y ]→U be a homotopy invariant. By definition, the invariant f has order at most r if the characteristic function of the rth Cartesian power of the graph of a continuous map a: X→ Y determines the value f([a]) Z-linearly. It is proved that, in the stable case (that is, when dim X > 2n-1, and Y is (n-1)-connected for some natural number n), for a finite cell complex X the order of the invariant f is equal to its degree with respect to the Curtis filtration of the group [X, Y ].