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A new method of pseudo-state discretization is proposed for the method ofcontinuum discretized coupled channels (CDCC) to deal with three-body breakupprocesses. We propose real- and complex-range Gaussian bases for thepseudo-state wave functions, and show that they form in good approximation acomplete set in the configuration space which is important for breakupprocesses.  Continuous S-matrix elements are derived with the approximate completenessfrom 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 MeVwith the satisfactory results. Possibility of application of the method tofour-body breakup processes is also discussed.Comment: 10 pages, 14 Postscript figures, uses REVTeX 4, submitted to Phys.  Rev.

New treatment of breakup continuum in the method of continuum discretized coupled channels