The two-body decays of the extra neutral boson Z(2) predicted by the minimal 3-3-1 model are analyzed. At the tree level, it can decay into standard model particles as well as exotic quarks and the new gauge bosons predicted by the model. The decays into a lepton pair are strongly suppressed, with Br(Z(2)-->l(+)l(-))approximate to10(-2) and Br(Z(2)-->(v) over bar (l)nu)approximate to10(-3). In the bosonic sector, Z(2) would decay mainly into a pair of bilepton gauge bosons, with a branching ratio below the 0.1 level. The Z(2) boson thus has a leptophobic and bileptophobic nature and it would decay dominantly into quark pairs. The anomaly-induced decays Z(2)-->Z(1)gamma and Z(2)-->Z(1)Z(1), which occur at the one-loop level, are studied. It is found that Br(Z(2)-->Z(1)gamma)approximate to10(-9) and Br(Z(2)-->Z(1)Z(1))approximate to10(-6) at most. As for the Z(2)-->W+W- and Z(2)-->Z(1)H decays, with H a relatively light Higgs boson, they are induced via Z'-Z mixing. It is obtained that Br(Z(2)-->W+W-)approximate to10(-2) and Br(Z(2)-->Z(1)H)approximate to10(-5). We also examine the flavor changing neutral current decays Z(2)-->tc and Z(2)-->tu, which may have branching fractions as large as 10(-3) and 10(-5), respectively, and thus may be of phenomenological interest.