Abstract: This work is a brief presentation of the theory based on the SU(3)(c) circle times SU(3)(L) circle times U(1)(X) gauge group in the presence of heavy leptons. Recent studies [1] have considered a set of four possible variants for the 3-3-1HL, whose content arises according to the so-denoted variable beta. Since it has been argued about the presence of stable charged particles in this sort of model, we divide the different sectors of the Lagrangian between universal and specific vertices, and conclude that the omission of beta-dependent terms in the potential may induce discrete symmetry for the versions defined by vertical bar beta vertical bar = root 3 . In the context of vertical bar beta vertical bar = 1/root 3, where the new degrees of freedom have the same standard electric charges, additional Yukawa interactions may create decay channels into the SM sector. Furthermore, motivated by a general consequence of the Goldstone theorem, a method of diagonalization by parts is introduced in the Scalar sector and provides a clarification on the definition of mass eigenstates. In summary, we develop the most complete set of terms allowed by the symmetry group and resolve their definitive pieces in order to justify the model description present in the literature.