  An improved analysis of the diphoton decay rate of the Higgs boson in the
Inert Doublet Model is presented together with critical discussion of the
results existing in the literature. For Higgs boson mass M_h equal 125 GeV, and
taking into account the following constraints: vacuum stability, existence of
the Inert vacuum, perturbative unitarity, electroweak precision tests and the
LEP bounds, we found regions in the parameter space where the diphoton rate is
enhanced. The resulting regions were confronted with the allowed values of the
Dark Matter mass. We found that significant enhancement in the two photon decay
of the Higgs boson is only possible for constrained values of scalar couplings
\lambda_3 hH+H-, \lambda_{345} hHH and masses of the charged scalar and the
Dark Matter particle. The enhancement above 1.3 demands the masses of H+ and H
to be less than 135 GeV (and above 62.5 GeV) and -1.46<\lambda_3,\lambda_{345}
<-0.24. In addition we analyzed the correlation of the diphoton and Z+photon
rates.
