The half-metallicity and the magnetism of the CoS2(001) surface are investigated by means of the all-electron full-potential linearized augmented plane wave method within the generalized gradient approximation. All three types of terminations were considered for the CoS2(001) surface: the Co-Term (Co terminated), the 2S-Term (removing the surface Co layer from the Co-Term), and the 1S-Term (removing the surface S layer from the 2S-Term). It is found that the half-metallicity and magnetism at the surface are closely related to the sulfur-sulfur (S-S) dimerization. The S-S dimer remains for the surface of 1S-Term and the surface retains the half-metallicity. However, the S-S dimers for the surfaces of the 2S-Term and the Co-Term are broken and the surfaces lose half-metallicity. The magnetic moments of the Co atoms at the surface of Co-Term and the subsurface of the 1S-Term are enhanced to 1.26 and 1.00 mu(B), while those of the inner (T-3) and (T-2) layers, i.e., the fourth and the third layers for the Co-Term, and 2S-Term are considerably reduced to 0.49 and 0.22 mu(B), respectively.