P-sets consists of an internal P-set X-(F) over bar and an outer Pset X-(F) over bar and has dynamic characteristics, which result from the internal dynamic characteristics on X-(F) over bar and the outer dynamic characteristics on X-(F) over bar. In order to extend the application of the P-sets, the paper proposes an X-(F) over bar-recursive binary tree through applying the dynamic characteristics for the P-set X-(F) over bar. Meanwhile, the paper provides the structures and characteristics for the (F) over bar -recursive binary tree, including some properties and theorems about the (F) over bar -recursive binary tree. The paper also gives the method of constructing (F) over bar -recursive binary tree. The (F) over bar -recursive binary tree has inward contraction characteristics and recursive characteristics. It can be used many research fields, such as information science and technology, artificial intelligence, knowledge discovery, as well as control theory and control engineering.