The catalytic decomposition of hydrazine using metallic nanoparticles has recently attracted considerable attention as this provides a promising means for highly efficient hydrogen release desired for a cleaner economy; however, the efficient catalytic nanoparticles model is still controversial. To shed further light on the optimal morphology of rhodium nanoparticles reported as the most efficient catalyst for this reaction, a more realistic nanocluster (Rh-n) model is implemented here to compare the adsorption energies of hydrazine on these nanoclusters using the density functional theory. These nanoclusters (Rh-n) comprise a varied number of Rh atom (n=13-201), with their pre-constructed shapes but further defined by the highest energy optimization. Our calculations unravel that the vertex atoms of an Rh-n nanocluster are the most favoured sites for N2H4 adsorption, in comparison with edge atoms or inner atoms of facets. Notably, the computed adsorption energies (E-ads) clearly exhibit a linear dependence on their sizes effective particle diameter (r), with the equation E-ads=-1.30+(-0.24) r established. Further calculations on the introduction of adatoms to the regular nanoclusters demonstrated that the stepped facet plays a decisive role in determining the adsorption energy. Moreover, the electronic structure and charge transfer calculations revealed the dative-type binding nature of the N-Rh bond. These results highlight the importance of a more realistic particle model used for such adsorption studies and provide new insights into the design and development of nanocatalysts for the decomposition of hydrazine.