  We present a novel method of smoothing discrete breakup cross sections
calculated by the method of continuum-discretized coupled-channels. The method
based on the complex scaling method is tested with success for $^{58}$Ni($d$,
$pn$) reaction at 80 MeV as an example of a three-body breakup reaction, and
applied to $^{12}$C($^6$He, $nn^4$He) reaction at 229.8 MeV as a typical
example of a four-body breakup reaction. The new method does not need to derive
continuum states of the projectile in order to evaluate the breakup cross
section as a smooth factor of the excitation energy of the projectile. Fast
convergence of the breakup cross section with respect to extending the
modelspace is confirmed. For the $^6$He breakup cross section, the resonant
component is separated from the non-resonant one.
