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A sequential fourth generation is known to be excluded because thenon-decoupling contribution to $\kappa_g$, the Higgs coupling modifier with agluon pair, is unacceptably large. Recently a new way to save the model wassuggested in the Type-II two Higgs doublet model: if the Yukawa couplings ofdown-type fermions have wrong-sign, the contributions from $t'$ and $b'$ to$\kappa_g$ are cancelled. We study the theoretical and experimental constraintson this model, focusing on the heavy Higgs bosons. Two constraining featuresare pointed out. First the exact wrong-sign limit does not allow the alignment,which makes the perturbative unitarity for the scalar-scalar scattering put theupper bounds on the heavy Higgs boson masses like $M_H, M_A \lesssim 920$ GeVand $M_{H^\pm} \lesssim 620$ GeV. Secondly, the Yukawa couplings of the fourthgeneration fermions to the heavy Higgs bosons are generically large as beingproportional to the heavy fermion mass and, for the down-type fermions, to$\tan\beta$ as well. The gluon fusion productions of $H$ and $A$ through thefourth generation quark loops become significant. We found that the current LHCdata on $pp \to Z Z$ for $H$ along with the theoretical and indirectconstraints exclude the model at leading order.

Confronting the fourth generation two Higgs doublet model with the phenomenology of heavy Higgs bosons