Two algorithms for many-body interaction energy decomposition within the Hartree-Fock approximation an presented, These two schemes, which are extensions of the two-body Kitaura-Morokuma (KM) analysis and the reduced variational space self-consistent-field(RVS SCF) method, decompose the interaction energy into electrostatic, exchange, polarization, and charge transfer components. The Hartree-Fock interaction energies for the optimum water dimer, trimer, and tetramer were analyzed in terms of two-, three-, and four-body terms of these individual components. Counterpoise calculations of the exchange and charge transfer components proposed by Tomasi were performed to estimate the basis set superposition errors. The results show that the three-body nonadditive terms of water trimer and tetramer are dominated by the polarization and charge transfer components at their optimized structures with various basis sets and that the four-body term of water tetramer is very small. The RVS SCF energy components, whose corresponding wave functions obey the Pauli exclusion principle, are better behaved than their counterparts in the KM analysis when the orbital interactions are strong.