  The simplest noncompact group SU(1,1),when introduced as a symmetry group of
the generations of quarks and leptons in the framework of a vector-like theory,
gives an excellent viewpoint on low energy physics. The minimal setup of the
scheme, however, gives phenomenologically unacceptable prediction on the Yukawa
coupling matrices. This suggests the higgs sector has richer structure than we
expect from the success of MSSM. The natural extension of the scheme, which has
doubled structure in the higgs sector, is formulated. The framework admits this
extension in a restrictive way. The possible patterns of Yukawa couplings are
classified and the expressions of the coupling matrices are presented.
