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For three generations of quarks, we show that one of quark mass matrices canbe transformed into either a Fritzsch form or a Branco-Silva-Marcos form, whilethe other is kept in the NNI basis. In these bases, quark mass matrices aredetermined unambiguously once quark masses and the CKM mixing are given.Comment: 12page

The Rephasing Freedom and the NNI Form of Quark Mass Matrices