In this paper, a pilot study regarding carotid atherosclerotic plaque instability using B-mode ultrasound (US) images was carried out. The fractal dimension of plaques obtained from ten symptomatic subjects (i.e., subjects having experienced neurological symptoms) as well as from nine asymptomatic subjects, was estimated using a novel method, called the kth nearest neighbour (KNN) method. The results indicated a significant difference, as per the fractal dimension, between the two groups, providing a significantly lower value for the asymptomatic group. Moreover, the phase of the cardiac cycle (systole/diastole) during which the fractal dimension was estimated had no systematic effect on the calculations. The fractal dimension of the plaques was also estimated using a well-known method, namely the box-counting (BC) method. No significant differences between the two groups, as per the fractal dimension, were observed using the BC method. The presented pilot study suggests that the fractal dimension, estimated by the proposed method, could be used as a single determinant for the discrimination of symptomatic and asymptomatic subjects. (E-mail: knikita@cc.ece.ntua.gr)