Abstract:  Let H be infinite Hilbert space. For any bounded linear operator A in H, and A(2)(P,Q) is (P,Q) outer generalized inverse of A, where P, Q are idempotent operators in H. By the method of operational partitioning, the existence and the explicit expression for A(2)(P,Q) are derived. Also, the reflexive law of A(2)(P,Q) is considered; As an application, a numerical example is given.

Key words: Hilbert space, reflexive, outer generalized inverse