In recent papers, the author has proved that
4
4
-webs
W(4,2,2)
{\text {W(4,2,2)}}
of codimension 2 and maximum
2
2
-rank on a
4
4
-dimensional differentiable manifold are exceptional in the sense that they are not necessarily algebraizable, while maximum
2
2
-rank
2
2
-codimensional
d
d
-webs
W(d,2,2),
d
>
4
{\text {W(d,2,2),}}d > 4
, are algebraizable. Examples of exceptional isoclinic webs W(4,2, 2) were given in those papers. In the present paper, the author proves that a polynomial nonisoclinic
3
3
-web
W(3,2,2)
{\text {W(3,2,2)}}
cannot be extended to a nonisoclinic
4
4
-web
W(4,2,2)
{\text {W(4,2,2)}}
and constructs an example of a nonisoclinic
4
4
-web
W(4,2,2)
{\text {W(4,2,2)}}
of maximum
2
2
-rank.