  A cross-bifix-free set of words is a set in which no prefix of any length of
any word is the suffix of any other word in the set. A construction of
cross-bifix-free sets has recently been proposed by Chee {\it et al.} in 2013
within a constant factor of optimality. We propose a \emph{trace partitioned}
Gray code for these cross-bifix-free sets and a CAT algorithm generating it.
