A language is called (elementary) biordered, shortened as (EBL) BL, if it is recognized by (a single idempotent) some idempotents of a monoid. In this paper, the sufficient and necessary conditions for a language to be (EBL) BL are given. Further, the concept of absolutely elementary biordered language (AEBL) is defined. The precise structure and the syntactic monoids of AEBLs are described. Some important relations among them are investigated. Finally, a structure of any BL is given via AEBLs.