  In this paper we study the linearizability problem for 3-webs on a
2-dimensional manifold. With an explicit computation based on the theory
developed in the paper "On the linearizability of 3-webs" (Nonlinear analysis
47, (2001) pp. 2643-2654), we examine a 3-web whose linearizability was claimed
in the same paper. We show that, contrary to the statement of the papers "On
the Blaschke conjecture for 3-webs" (arXiv: math.DG/0411460) and "On
linearization of planar three-webs and Blaschke's conjecture", (C.R.Acad. Sci.
Paris, Ser. I. vol. 341. num 3 (2005)), this particular web is linearizable. We
compute explicitly the affine deformation tensor and the corresponding flat
linear connection adapted to the web which linearizes it.
