  We study the contribution of charged Higgs boson to the rare decay of the top
quark t->q+WZ (q=d,s,b) in models with Higgs sector that includes doublets and
triplets. Higgs doublets are needed to couple charged Higgs with quarks,
whereas the Higgs triplets are required to generate the non-standard vertex HWZ
at tree-level. It is found that within a model that respect the custodial SU(2)
symmetry and avoids flavour changing neutral currents by imposing discrete
symmetries, the decay mode t->b+WZ, can reach a branching ratio of order
0.0178, whereas the decay modes t->(d,s)+WZ, can reach a similar branching
ratio in models where flavour changing neutral currents are suppressed by
flavour symmetries.
