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The mass splittings for the Majorana neutrinos in the exact solution of aparticular 3-3-1 gauge model are computed here in detail. Since both$\sin^{2}\theta_{13}\simeq0$ and the mass splittings ratio$r_{\Delta}\simeq0.033$ are taken into account, the analytical calculationsseem to predict an inverted mass hierarchy and a mixing matrix with a texturebased on a very close approximation to the bi-maximal mixing. The resultingformulas for the mass squared differences can naturally accomodate theavailable data if the unique free parameter ($a$) gets very small values($\sim10^{-15}$). Consequently, the smallness of the parameter requires(according to our method) a large breaking scale $<\phi>\sim10^{6}-10^{7}$ TeVin the model. Hence, the results concerning the neutrino mass splittings maylead to a more precise tuning in the exact solution of the 3-3-1 model ofinterest, being able - at the same time - to recover all the Standard Modelphenomenology and predict the mass spectrum of the new gauge bosons$Z^{\prime},X,Y$ in accordance with the actual data. The minimal absolute massin the neutrino sector is also obtained - $m_{0}\simeq0.0035$ eV - in the caseof our suitable approximation for the bi-maxcimal mixing.Comment: 10 pages, no figure

NEUTRINO MASS SQUARED DIFFERENCES IN THE EXACT SOLUTION OF A 3-3-1 GAUGE MODEL WITHOUT EXOTIC ELECTRIC CHARGES