His argument for that is based on research that shows that the production of the cilium in eukaryotes requires the operation of another cellular system known as intraflagellar transport, or IFT. Thus, Behe claims, both the cilium and the IFT are irreducibly complex, which is why he labels that section Irreducible Complexity Squared. He declares:

IFT exponetially increases the difficulty of explaining the irreducibly complex cilium. It is clear from careful experimental work with all ciliated cells that have been examined, from alga to mice, that a functioning cilium requires a working IFT.12 The problem of the origin of the cilium is now intimately connected to the problem of the origin of IFT. Before its discovery we could be forgiven for overlooking the problem of how a cilium was built. Biologists could vaguely wave off the problem, knowing that some proteins fold by themselves and associate in the cell without help. Just as a century ago Haeckel thought it would be easy for life to originate, a few decades ago one could have been excused for thinking it was probably easy to put a cilium together; the piece could probably just glom together on their own. But now that the elegant complexity of IFT has been uncovered, we can ignore the question no longer.

Wow, double the irreducible complexity! You can't build cilia without a functioning IFT, so now you have to explain both the origin of the IFT and the origin of cilia. Except that, as Nick shows, this claim is just plain false. Just as his claim in his earlier book that every single factor in the blood clotting cascade must be present in order to function was easily disproven by pointing to dolphins, which lack Factor XII (Hagemann factor) yet still have blood that clots), this claim is easily disproven by showing that, in the real world, there exist organisms which have cilia but do not have the IFT.

Nick shows a chart and offers a citation showing that there is an existing organism that has a cilium but does not have IFT, an organism in a group called Apicomplexans. Specifically, a parasitic organism in that group. More specifically, a parasite known as Plasmodium falciparum. You might know it by its better known name: malaria. Yes, the very organism that Behe spends much of his book using as evidence of IC actually disproves his claim about the cilia/IFT system being irreducible. Oops.