This paper is mainly devoted to proving the four equivalent defining properties of a CBA(κ) space. The proof is based on an interesting tool we established which describes the cyclical five-step deformation procedure for quadrangles in the model 2-plane S2κ ,including the limit shape of each step. As a byproduct we give a complete list of cyclical deformation procedures for all kinds of quadrangles on S21 . At last we make a contrast of geometric properties of CBA with CBB spaces,including a comparison between their defining properties and a discussion about Alexandrov’s Lemma.