  We present a method for smoothing discrete breakup $S$-matrix elements
calculated by the method of continuum-discretized coupled-channels (CDCC). This
smoothing method makes it possible to apply CDCC to four-body breakup
reactions. The reliability of the smoothing method is confirmed for two cases,
$^{58}$Ni($d$, $p n$) at 80 MeV and the $E1$ transition of $^6$He. We apply
CDCC with the smoothing method to $^6$He breakup reaction at 22.5 MeV.
Multi-step breakup processes are found to be important.
