Neural oscillations are critical to understanding the synchronisation of neural activities and their relevance to neurological disorders. For instance, the amplitude of beta oscillations in the subthalamic nucleus has gained extensive attention, as it has been found to correlate with medication status and the therapeutic effects of continuous deep brain stimulation in people with Parkinson's disease. However, the frequency stability of subthalamic nucleus beta oscillations, which has been suggested to be associated with dopaminergic information in brain states, has not been well explored. Moreover, the administration of medicine can have inverse effects on changes in frequency and amplitude. In this study, we proposed a method based on the stationary wavelet transform to quantify the amplitude and frequency stability of subthalamic nucleus beta oscillations and evaluated the method using simulation and real data for Parkinson's disease patients. The results suggest that the amplitude and frequency stability quantification has enhanced sensitivity in distinguishing pathological conditions in Parkinson's disease patients. Our quantification shows the benefit of combining frequency stability information with amplitude and provides a new potential feedback signal for adaptive deep brain stimulation.