A saccade is one of the characteristic types of eye movements. The accurate detection and location of saccades in the signal representing the movement activity of the eyes are essential in medical applications. The main purpose of this paper is to present a new, robust approach to the detection of saccadic eye movements. The procedure is based on a so-called detection function, which is the result of the electronystagmographic (ENG) myriad signal filtering, nonlinear operation, and fuzzy median clustering. Smooth peaks of the detection function waveform correspond to the location of saccades in the ENG signal. The median fuzzy clustering-based method allows for calculating the amplitude threshold of the detection function, which improves the accurate saccade recognition. Both of these robust methods provide a two-step protection against outliers. The proposed algorithm was tested using artificial as well as real optokinetic nystagmus signals under different noise conditions. The results show the usefulness of the procedure when the precise detection and location of saccades are necessary.