  Integrable couplings are associated with non-semisimple Lie algebras. In this
paper, we propose a new method to generate new integrable systems through
making perturbation in matrix spectral problems for integrable couplings, which
is called the `completion process of integrable couplings'. As an example, the
idea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrable
coupling. Each equation in the resulting hierarchy has a bi-Hamiltonian
structure furnished by the component-trace identity.
