The eigenvalues and mixing angles in the Zee model are investigated
parameter-independently. When we require |\Delta m^2_{12}/\Delta m^2_{23}| \ll
1 in order to understand the solar and atmospheric data simultaneously, the
only solution is one which gives bi-maximal mixing. It is pointed out that the
observed values \sin^2 2\theta_{solar} \simeq 0.66 in the MSW LMA solution
cannot be explained within the framework of the Zee model, because we derive a
severe constraint on the value of \sin^2 2 \theta_{solar}, \sin^2 2
\theta_{solar} \geq 1 -(1/16)(\Delta m^2_{solar}/\Delta m^2_{atm})^2.Comment: Latex file, 10 pages, 1 figure, explanations and references added,
typos corrected, to be published in Phys.Rev.
