A quasielastic neutron scattering (QENS) experiment is a particular technique that endeavors to define a relationship between time and space for the diffusion dynamics of atoms and molecules. However, in most cases, analyses of QENS data are model dependent, which may distort attempts to elucidate the actual diffusion dynamics. We have developed a method for processing QENS data without a specific model, wherein all modes can be described as combinations of the relaxations based on the exponential law. By this method, we can obtain a distribution function B(Q,Γ), which we call the mode-distribution function (MDF), to represent the number of relaxation modes and distributions of the relaxation times in the modes. The deduction of MDF is based on the maximum entropy method and is very versatile in QENS data analysis. To verify this method, reproducibility was checked against several analytical models, such as that with a mode of distributed relaxation time, that with two modes closely located, and that represented by the Kohlrausch-Williams-Watts function. We report the first application to experimental data of liquid water. In addition to the two known modes, the existence of a relaxation mode of water molecules with an intermediate time scale has been discovered. We propose that the fast mode might be assigned to an intermolecular motion and the intermediate motion might be assigned to a rotational motion of the water molecules instead of to the fast mode.