  We present the explicit expressions for the matrix product operator (MPO)
representation for the local conserved quantities of the Heisenberg chain. The
bond dimension of the MPO grows linearly with the locality of the charges. The
MPO has more simple form than the local charges themselves, and their Catalan
tree patterns naturally emerge from the matrix products. The MPO representation
of local conserved quantities is generalized to the integrable $\mathrm{SU}(N)$
invariant spin chain.
