  We construct, to the first two non-trivial orders, the next conserved charge
in the su(2|3) sector of N=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.
