  In this note we straightforwardly derive and make use of the quantum R-matrix
for the su(2|2) SYM spin-chain in the manifest su(1|2)-invariant formulation,
which solves the standard quantum Yang-Baxter equation, in order to obtain the
correspondent (undressed) classical r-matrix from the first order expansion in
the ``deformation'' parameter 2 \pi / \sqrt{\lambda}, and check that this last
solves the standard classical Yang-Baxter equation. We analyze its bialgebra
structure, its dependence on the spectral parameters and its pole structure. We
notice that it still preserves an su(1|2) subalgebra, thereby admitting an
expression in terms of a combination of projectors, which spans only a subspace
of su(1|2) \otimes su(1|2). We study the residue at its simple pole at the
origin, and comment on the applicability of the classical Belavin-Drinfeld type
of analysis.
