Kinesthetic motor imagery (KMI) tasks induce brain oscillations over specific regions of the primary motor cortex within the contralateral hemisphere of the body part involved in the process. This activity can be measured through the analysis of electroencephalographic (EEG) recordings and is particularly interesting for Brain-Computer Interface (BCI) applications. The most common approach for classification consists of analyzing the signal during the course of the motor task within a frequency range including the alpha band, which attempts to detect the Event-Related Desynchronization (ERD) characteristics of the physiological phenomenon. However, to discriminate right-hand KMI and left-hand KMI, this scheme can lead to poor results on subjects for which the lateralization is not significant enough. To solve this problem, we propose that the signal be analyzed at the end of the motor imagery within a higher frequency range, which contains the Event-Related Synchronization (ERS). This study found that 6 out of 15 subjects have a higher classification rate after the KMI than during the KMI, due to a higher lateralization during this period. Thus, for this population we can obtain a significant improvement of 13% in classification taking into account the users lateralization profile.