We propose to implement the Natural Flavor Conservation criterion in the two
Higgs doublet model (2HDM) to an extra U(1)_H gauge symmetry for Higgs flavor,
assuming two Higgs doublets carry different U(1)_H charges. Then one can easily
avoid the tree level FCNC from neutral Higgs mediations using local gauge
symmetries, instead of softly broken ad hoc Z_2 symmetry, and the pseudoscalar
boson could be eaten by extra Z_H boson. Imposing the anomaly cancellation, we
find that the U(1)_H in the Type-II and Type-IV 2HDM's become leptophobic and
leptophilic, respectively. For the Type-I case, U(1)_H depends on two
parameters, and some simple cases include U(1)_H = U(1)_{B-L}, U(1)_R, or
U(1)_Y. We sketch qualitative phenomenology of these models.Comment: 7 pages, version published in Phys. Lett.