We present a new pruning procedure  on discrete trees by adding marks on
the nodes  of trees. This procedure  allows us to construct  and study a
tree-valued Markov process (G(u))  by pruning Galton-Watson trees and an
analogous  process   (G'(u))  by  pruning  a   critical  or  subcritical
Galton-Watson tree conditioned to be infinite. Under a mild condition on
offspring distributions, we  show that the process (G(u))  run until its
ascension  time has  a representation  in  terms of  (G'(u)). A  similar
result was obtained  by Aldous and Pitman (1998) in  the special case of
Poisson offspring distributions where they considered uniform pruning of
Galton-Watson trees by adding marks on the edges of trees.