Employing first-principles calculations, we investigate the relaxations of a clean and Co decorated Pt step- edge on a (111) microfaceted (111) surface. The visibility of the relaxation in scanning tunneling microscopy (STM) images is discussed. We calculate the magnetocrystalline anisotropy energy (MAE) of the Co decorated vicinal surface with and without relaxation effects taken into account and compare our results to experiments done for Co/ Pt(997) and to previous calculations with different geometries simulating the vicinal surface. As compared to the unrelaxed case, the relaxation of the Co chain towards the substrate enhances the contribution of Pt to the MAE and turns the easy axis more in the direction of the surface plane.