We describe the calculation of the one-loop corrections to $H \to \gamma \gamma$ and $g g \to H$ within the four-dimensional unsubtraction/loop-tree duality (FDU/LTD) approach. The fact that these corrections are both IR and UV finite is not enough to perform the computation without a proper regularization of the intermediate steps. We show how the FDU/LTD method unambiguously leads to the proper result with a pure four-dimensional representation of the loop amplitude. Moreover, this method allows us to obtain very compact expressions which share the same functional structure independently of the particles circulating the loop. Besides this, asymptotic expansions for the low and high mass regime naturally arise as a consequence of the smoothness of the integrands obtained to describe the amplitudes.