  The paper studies the structure of restricted Leibniz algebras. More
specifically speaking, we first give the equivalent definition of restricted
Leibniz algebras, which is by far more tractable than that of a restricted
Leibniz algebras in [6]. Second, we obtain some properties of $p$-mappings and
restrictable Leibniz algebras, and discuss restricted Leibniz algebras with
semisimple elements. Finally, Cartan decomposition and the uniqueness of
decomposition for restricted Leibniz algebras are determined.
