  Based on the Connes--Kreimer Hopf algebra of rooted trees, the rooted tree
maps are defined as linear maps on noncommutative polynomial algebra in two
indeterminates. It is known that they induce a large class of linear relations
for multiple zeta values. In this paper, we investigate some basic algebraic
properties of rooted tree maps by relating to the harmonic algebra. We also
characterize the antipode maps as the conjugation by the special map $\tau$.
