  According to Alain H\'enaut, a planar 4-web is called Nakai's web if the
cross-ratio of the tangents to the four foliations at each point is constant
and if it has no hexagonal 3-subweb. We prove that Nakai's webs have rank 0 or
1. We give examples with rank 1 and present a universal way to build such
examples.
