Abstract: In this paper, the polynomial solution of the Lenard's recurise equation associatedwith coupled Harry-Dym (CHD) hierarchy is derived,and it is proved that every solution ofstationary CHD equation has a integrable Bargmann coordinate. Finally Poisson structure anddynamical r-matrix for the restricted system are presented.

Key words: Stationary equation, Bargmann coordinate, restricted system, r-matrix, Poisson structure