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Integrable couplings are associated with non-semisimple Lie algebras. In thispaper, we propose a new method to generate new integrable systems throughmaking perturbation in matrix spectral problems for integrable couplings, whichis called the `completion process of integrable couplings'. As an example, theidea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrablecoupling. Each equation in the resulting hierarchy has a bi-Hamiltonianstructure furnished by the component-trace identity.

Completion of the Ablowitz-Kaup-Newell-Segur integrable coupling