Summary: The basic formula of an amphibole is completely defined by stating the number of sodium atoms in X positions and the numbers of aluminium atoms in Y and Z. These three numbers are coordinates in a compositional space that can easily be represented. The alkali amphiboles are re-defined as having at least one atom of sodium in X in the basic formula unit. A systematic nomenclature for the calciferous and alkali amphiboles is suggested using existing end-member names.