This paper introduces the concept of an extended pseudo-biorthogonal basis" (EPBOB), which is a generalization of the concepts of an orthonormal (OB), a biorthonormal (BOB), a pseudo-orthogonal (POB), and a pseudo-biorthogonal (PBOB) bases. Let HN be a subspace of a Hilbert space H. The concept of EPBOB says that we can always construct a set of 2M (MN) elements of H but not necessarily all in HN such that like BOB any element f in HN can be expressed by fMΣm=1(f,φ*m)φm. For a better understanding and a wide application of EPBOB, this paper provides their characterization and shows how they preserve the formalism of BOB. It also shows how to construct them.