Magnetism in clusters having upto 15 atoms of non-magnetic element, Rh is studied using the ab initio ultrasoft pseudopotential method and generalized gradient approximation for the exchangecorrelation energy. The lowest energy structures are found to have no atom at the center upto n= 13 and have low symmetries. The well known icosahedral structure for 13 atoms does not have the lowest energy. A transition to more compact structures with an atom at the center occurs beyond 13 atoms. The calculated magnetic moments are in better agreement with experiments than obtained before. An H atom on these clusters favors a bridge side and generally reduces the magnetic moment.