Eye movements are a relatively novel data source for biometric identification. When video cameras applied to eye tracking become smaller and more efficient, this data source could offer interesting opportunities for the development of eye movement biometrics. In this paper, we study primarily biometric identification as seen as a classification task of multiple classes, and secondarily biometric verification considered as binary classification. Our research is based on the saccadic eye movement signal measurements from 109 young subjects. In order to test the data measured, we use a procedure of biometric identification according to the one-versus-one (subject) principle. In a development from our previous research, which also involved biometric verification based on saccadic eye movements, we now apply another eye movement tracker device with a higher sampling frequency of 250 Hz. The results obtained are good, with correct identification rates at 80-90% at their best.