A new version of a lattice fluid hydrogen bonding (LFHB) model is presented to improve the predictions of the thermodynamic properties of associating fluids. The model utilizes the physical contribution to the free energy in the statistical association fluid theory (SAFT). The association term is described by the local density instead of the bulk density, which was used in the original versions of the theory. With these two modifications, predictions are improved significantly for hard sphere molecules with association sites and for real molecules. Results are presented for the densities and vapor pressures of pure water and 1-alkanols, and for the phase equilibria and association of a mixture of benzophenone and water. The predicted degree of hydrogen bonding for pure supercritical water compares quite favorably with molecular dynamics simulation data. Unlike the case for the SAFT model. association depends upon pressure in the new model because of the volume change upon hydrogen bond formation.