Different ansa¨tze for the breaking of the flavor permutational symmetry according toSL(3)⊗SR(3)⊃SL(2)⊗SR(2)give different Hermitian mass matrices which differ in the symmetry breaking pattern. In this work we obtain a clear and precise indication on the preferred symmetry breaking pattern. The preferred pattern allows us to compute theCKMmixing matrix, the Jarlskog invariantJ, and the three inner angles of the unitarity triangle in terms of four quark mass ratios and theCPviolating phase &Fgr;. Excellent agreement with the experimentally determined absolute values of the entries in theCKMmatrix is obtained for&Fgr;=90°.The corresponding computed values of the Jarlskog invariant and the inner angles areJ=3.00×10−5,&agr;=84°,&bgr;=24°and&ggr;=72°in very good agreement with current data onCPviolation in the neutral kaon-antikaon system and oscillations in theBs°−B¯s°system. ©1999 American Institute of Physics.