We extend the T violating model of the paper on "Hidden symmetry of the CKM and neutrino mapping matrices" by assuming its T-violating phases X↑ and X↓ to be large and the same,with X = X↑= X↓.In this case,the model has 9 real parameters:α↑,β↑T,ξ↑,η↑ for the ↑-quark sector,α↑,β↑T,ξ↑,η↑ for the ↓sector and a common X.We examine whether these nine parameters are compatible with ten observables:the six quark masses and the four real parameters that characterize the CKM matrix (i.e.,the Jarlskog invariant J and three Eulerian angles).We find that this is possible only if the T violating phase X is large,between -120° to -135°.In this strong T violating model,the smallness of the Jarlskog invariant J ≌ 3 × 10-5 is mainly accounted for by the large heavy quark masses,with mc/mt＜ ms/mb≈ 0.02,as well as the near complete overlap of t and b quark,with (c|b)=-0.04.