  We introduce two square-tiled surfaces, one with $8$ squares inside $\Omega
\mathcal{M}_3(2,2)$, and the other with $9$ squares inside $\Omega
\mathcal{M}_4(3,3)$, respectively. In these examples, the dimensions of the
isotropic subspaces (in absolute homology) generated by the waist curves of the
maximal cylinders in any fixed rational direction are $2$ and $3$ respectively.
Hence, a geometrical criterion of G. Forni for the non-uniform hyperbolicity of
Kontsevich-Zorich (KZ) cocycle can not be applied to these examples.
Nevertheless, we prove that there are no vanishing exponents and the spectrum
is simple for these two square-tiled surfaces. In particular, the non-vanishing
of exponents of KZ cocycle for a regular measure doesn't imply that the support
of this measure contains a completely periodic surface whose waist curves of
maximal cylinders generates a Lagrangian subspace in its absolute homology.
