  Let T d (n) be the set of d-ary rooted trees with n internal nodes. We give a
method to construct a sequence (t n , n $\ge$ 0) where, for any n $\ge$ 1, t n
has the uniform distribution in T d (n), and t n is constructed from t n--1 by
the addition of a new node, and a rearrangement of the structure of t n--1.
This method is inspired by R{\'e}my's algorithm which does this job in the
binary case, but it is different from it. This provides a method for the random
generation of a uniform d-ary tree in T d (n) with a cost linear in n.
