Abstract
We construct, to the first two non-trivial orders, the next
conserved charge in the su(2|3) sector of 
= 4 Super
Yang-Mills theory. This represents a test of integrability in a
sector where the interactions change the number of sites of the
chain. The expression for the charge is completely determined by the
algebra and can be written in a diagrammatic form in terms of the
interactions already present in the hamiltonian. It appears likely
that this diagrammatic expression remains valid in the full theory
and can be generalized to higher loops and higher charges thus
helping in establishing complete integrability for these dynamical
chains.
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