The development of new approaches to detect motor-related brain activity is key in many aspects of science, especially in brain-computer interface applications. Even though some well-known features of motor-related electroencephalograms have been revealed using traditionally applied methods, they still lack a robust classification of motor-related patterns. Here, we introduce new features of motor-related brain activity and uncover hidden mechanisms of the underlying neuronal dynamics by considering event-related desynchronization (ERD) of μ-rhythm in the sensorimotor cortex, i.e., tracking the decrease of the power spectral density in the corresponding frequency band. We hypothesize that motor-related ERD is associated with the suppression of random fluctuations of μ-band neuronal activity. This is due to the lowering of the number of active neuronal populations involved in the corresponding oscillation mode. In this case, we expect more regular dynamics and a decrease in complexity of the EEG signal recorded over the sensorimotor cortex. In order to support this, we apply measures of signal complexity by means of recurrence quantification analysis (RQA). In particular, we demonstrate that certain RQA quantifiers are very useful to detect the moment of movement onset and, therefore, are able to classify the laterality of executed movements.