The translational and rotational diffusion coefficients and the dielectric spectrum of water at the ambient condition are calculated using the exponential memory model previously proposed by us. The translational diffusion coefficient is in good agreement with experiments and computer simulations. However, the rotational diffusion and dielectric relaxation of the present theory are about ten times as fast as those of experiments. In order to clarify the origin of the disagreement, the memory kernel is directly obtained from the molecular-dynamics simulation and compared with the exponential model. It is found that the long-time part of the memory kernel, which is not considered in the exponential model, is dominant in the rotational diffusion and the dielectric relaxation of water.