  The one-loop calculation of the amplitude for the Higgs decay
H-->\gamma\gamma\ due to virtual W's in the unitary gauge is presented. As the
Higgs does not directly couple to the massless photons, the one-loop amplitude
is finite. The calculation is performed in a straightforward way, without
encountering divergences. In particular, artifacts like dimensional
regularization are avoided. This is achieved by judiciously routing the
external momenta through the loop and by combining the integrands of the
amplitudes before carrying out the integration over the loop momentum. The
present result satisfies the decoupling theorem for infinite Higgs mass, and is
thus different from the earlier results obtained in the \xi=1 gauge using
dimensional regularization. The difference between the results is traced to the
use of dimensional regularization.
