  We prove that - even at a low TeV scale - the canonical seesaw mechanism can
be naturally implemented in the exact solution of a particular 3-3-1 gauge
model, since a very small alteration $\epsilon$ in the parameter matrix of the
Higgs sector is taken into account. Therefore, this new parameter can act as an
appropriate mass source for neutrinos, while - due to the main parameter $a$ -
all the previously achieved results in the exact solution of the model are
recovered. Moreover, this mathematical artifice does separate the boson mass
spectrum from the neutrino mass issue, hence giving more flexibility in tuning
the model. Possible phenomenological results and their implications - such as
dark matter plausible candidates that can occur - are also briefly discussed.
