A new type of bonding, termed anti-hydrogen bond, is identified in the benzene dimer and other carbon proton donor complexes from correlated ab initio computations. Gradient optimization of the benzene dimer at the MP2/6-31G* and MP2/6-31G** levels shows a shortening of the C-H bond of the proton donor and a blue-shift of the corresponding C-H stretching frequency. The harmonic C-H stretching vibrational frequency shift agrees well with that evaluated for various anharmonic approaches. The blue-shift of the C-H stretching frequency was also found in the case of benzene complexes with other carbon proton donors, CH4 and CHCl3. The anti-H-bonds are expected to be very significant for the structure and dynamics of biomolecules.