A simple extension of the Standard Model (SM), based on the gauge group $SU(3)_Cotimes SU(3)_Lotimes U(1)_Y$ with $Y$ being the hypercharge, is considered. We show that, by imposing an approximate global $SU(2)_Ltimes SU(2)_R$ custodial symmetry at the SM energy scale, the $Z-Z$ mixing is absent at tree level and the value of the $rho$ parameter can be kept close to one. Tree-level flavor-changing neutral currents are also reduced to three particles, namely $Z$, a CP-odd Higgs and a CP-even Higgs. The model predicts new leptons with electric charges of $pm 1/2e$ and new quarks with $pm 1/6e$ charges as well as new gauge and scalar bosons with $pm 1/2e$ charges. Electric charge conservation requires that one of them must be stable. Their masses are unfortunately free parameters.
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