The magnetism induced by D3-symmetry tetra-vacancy defects in graphene is investigated using first principles calculations. We find that the D3-symmetry tetra-vacancy defects cause remarkable lattice distortion, which significantly alters the electronic structures and magnetic properties of graphene. Moreover, the Lieb's theorem cannot be used because the bipartite symmetry is broken locally by lattice relaxation. If the dangling bonds around vacancies are passivated by the sp(2) hydrogen saturation, the lattice distortion is suppressed. Both the Lieb's theorem and tight-binding method can thus be used. (C) 2011 Elsevier B. V. All rights reserved.