We present a lattice model to study the “decoration” with the adsorbates on the stepped surface together with the step bunching induced by adsorbates. The model is the modified restricted solid-on-solid model coupled with Ising system (mRSOS-I model), where the energy reduction of the lateral bonds between the adsorbates on the different height of the surfaces is taken into consideration. We show, by Monte Carlo method, that the reduction factor ζ is one of the key parameter for the decoration on the stepped surface in addition to another key parameter of the interplay factor α, which we previously introduced in the original RSOS-I model. The deposited islands appear from the down side, the upper side, or the both sides of the steps depending on the values of ζ and α. [DOI: 10.1380/ejssnt.2009.39]