The decomposition of the movement of the eye into different categories is critical to their study. According to the algorithm used, some movements may significantly be over or under estimated. The two most important movements (saccade, swift movement and fixation, when the eye remains on the same position to capture information) are well characterized and usually properly identified by most algorithms, however in the context of writing, some other movements cannot be characterized as fixations or saccades. These movements may either be considered as microsaccades or slow movements which are actually close to saccades of fixations respectively but without completely sharing their characteristics. None of the algorithms available for eye movements classification can handle all the four movements. Some of them tend to first identify fixations by the barycenter method while others first identify saccades by the mean of speed. The approach used here is different as movements are first decomposed into elementary movements according to the acceleration scheme before they are merged. This new approach allows a better identification of each of the 4 kinds of movements.