We perform a complete calculation at the one-loop level for the Zggg and Zggg couplings in the context of the minimal 331 model, which predicts the existence of a new Z gauge boson and new exotic quarks. Bose symmetry is exploited to write a compact and manifest SU_C(3)-invariant vertex function for the Vggg (V=Z,Z) coupling. Previous results on the $Zto ggg$ decay in the standard model are reproduced. It is found that this decay is insensitive to the effects of the new exotic quarks. This in contrast with the $Zto ggg$ decay, which is sensitive to both the standard model and exotic quarks, whose branching ratio is larger than that of the $Zto ggg$ transition by about a factor of 4.
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