Within the frame of the ABCD formulation for the propagators in a time-dependent quantum system, the ABCD law has been extended to the so-called effective ABCD system in which the effective beam quality factor is conservative. We discussed the system as the propagation of the atom laser beam. The effective beam quality factor and the effective parameter are introduced to obtain the effective ABCD formulation of the propagators by means of Heisenberg picture. The atom-atom interactions in the atom laser beam make the beam quality factor nonconservative, and thus the effective beam quality factor can describe the combined effect of the beam quality factor and the atom-atom interaction.