  In the standard model (SM) of electroweak interactions, CP noninvariance
arises from the nonzero phase in the CKM matrix. Its contribution to the quark
electric dipole moment (EDM) vanishes surprisingly at two loop order. This
makes the quark EDM extremely small in the SM. In this paper, we consider the
two Higgs doublet extension of the SM and assume that CP noninvariance is still
encoded in the CKM matrix. We calculate the charged Higgs boson contribution to
the quark EDM which naively should be of order
$eG_F^2\tilde{\delta}(4\pi)^{-4}m_{u(d)}m_t^2m_b^2m_H^{-2}$ for the up (down)
quark with possible enhancement factors of $\tan^2\beta$. Here $\tilde{\delta}$
is the rephasing invariant of CP violation. However, contrary to the above
naive expectation, we find that the charged Higgs boson contribution vanishes
strictly at two loop order. We show explicitly how this comes about and
explains how it is related to the general form of Yukawa couplings in a
spontaneously broken gauge theory.
