The surface localized and resonance states of unrelaxed and relaxed SiC(110) zinc-blende surfaces have been investigated within the local density approximation of density functional theory (DFT), employing a first-principles full-potential self-consistent linear muffin-tin orbital (LMTO) method using a thicker (thirteen layer) slab. Intrinsic surface states appear in the fundamental energy gap for the unrelaxed surface. We have allowed non-bond-length-conserving relaxation of the surface atoms to obtain the minimum energy configuration. The shift in the surface states arising from the relaxation of atoms is small in comparison to other studied heteropolar covalent semiconductors because of the smaller value of the relaxation angle of the SiC(110) surface. New surface states have been predicted in the valence band region. The present atomic geometry is somewhat different from other theoretical results. We observe an inward displacement of the Si cation and an outward displacement of the C anion both parallel and perpendicular to the surface, different from the results of Sabisch et al. No experimental data are available for comparison.