  A new method of pseudo-state discretization is proposed for the method of
continuum discretized coupled channels (CDCC) to deal with three-body breakup
processes. We propose real- and complex-range Gaussian bases for the
pseudo-state wave functions, and show that they form in good approximation a
complete set in the configuration space which is important for breakup
processes.
  Continuous S-matrix elements are derived with the approximate completeness
from discrete ones calculated by CDCC.
  Accuracy of the method is tested quantitatively for two realistic examples,
d+$^{58}$Ni scattering at 80 MeV and $^{6}$Li+$^{40}$Ca scattering at 156 MeV
with the satisfactory results. Possibility of application of the method to
four-body breakup processes is also discussed.
