In the microscopic point of view, a decay rate of the nematic liquid crystalline order is formulated in a tractable form on the basis of a projection method, which is calculated by a Monte Carlo simulation of the Gay-Berne particle system. Three types of systems with different particle lengths are studied, where at a sampling during early stage of relaxation process, the decay rate is shown to increase as the length of the particle becomes short. At the system of particles of length with 3 times of a diameter, remarkable increase is observed at a transition to a disordered phase. The relaxation process of an order parameter is also simulated simultaneously in place of an experiment, from which the decay rate at the system with 3 times length is tentatively obtained as a macroscopic estimate by fitting the Monte Carlo curve of the order parameter to an exponential function. Both estimates of the decay rate are compared, where the correspondence is qualitatively good.