We observe that the invariance of neutrino mixing matrix under the simultaneous discrete transformations \nu 1 , \nu 2 , \nu 3 \rightarrow -\nu 1 , -\nu 2 , \nu 3 and \nu e, \nu \mu , \nu \tau \rightarrow -\nu e , \nu \tau , \nu \mu (neutrino ``horizontal conjugation'') characterizes (as a sufficient condition for it) the familiar bilarge form of neutrino mixing matrix, favored experimentally at present. Thus, the mass neutrinos \nu 1, \nu 2 , \nu 3 get a new quantum number, covariant with respect to their mixings into the flavor neutrinos \nu e, \nu \mu , \nu \tau (neutrino ``horizontal parity'' equal to -1, -1,1, respectively). The ``horizontal parity'' turns out to be embedded in a group structure consisting of some Hermitian and real 3\times 3 matrices \mu 1, \mu 2 , \mu 3 and \varphi 1, \varphi 2 , \varphi 3 , forming pairs interconnected through neutrino mixings. They generate some discrete transformations of mass and flavor neutrinos, respectively, in such a way that the group relations \mu 1 \mu 2 = \mu 3 (cyclic) and \varphi 1 \varphi 2 = \varphi 3 (cyclic) hold, while \mu a \mu b = \mu b \mu a and \varphi a \varphi b = \varphi b \varphi a . Then, for instance, the \mu 3 matrix may be chosen equal to the ``horizontal parity''.
PACS numbers: 12.15.Ff, 14.60.Pq, 12.15.Hh
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