We consider the height process of a L\'{e}vy process with no negative jumps,
and its associated continuous tree representation. Using tools developed by
Duquesne and Le Gall, we construct a fragmentation process at height, which
generalizes the fragmentation at height of stable trees given by Miermont. In
this more general framework, we recover that the dislocation measures are the
same as the dislocation measures of the fragmentation at node introduced by
Abraham and Delmas, up to a factor equal to the fragment size. We also compute
the asymptotic for the number of small fragments
