The three-body decays of a heavy Higgs H --> ttZBAR, H --> tbWBAR- + c.c. and of a heavy top t --> bW + H are studied in the context of the Standard Model. The common feature of these decay channels is the relative big coupling constant of the Higgs particle to the top quark. Indeed within a certain range of the masses M(H), m(t) we find that branching ratios of the order O(10(-3)) are possible for the decays H --> ttZBAR and t --> bW + H. The decay width GAMMA(H --> tbWBAR-) as a function of M(H) and m(t) is investigated below the 2m(t) threshold (M(H) < 2m(t)) and is found to have an interesting behavior just near this threshold.