  Considering a random binary tree with $n$ labelled leaves, we use a pruning
procedure on this tree in order to construct a $\beta(3/2,1/2)$-coalescent
process. We also use the continuous analogue of this construction, i.e. a
pruning procedure on Aldous's continuum random tree, to construct a continuous
state space process that has the same structure as the $\beta$-coalescent
process up to some time change. These two constructions unable us to obtain
results on the coalescent process such as the asymptotics on the number of
coalescent events or the law of the blocks involved in the last coalescent
event.
