Removing the contribution of dispensable mental activities dispersed across the electroencephalogram (EEG) signal improves the interpretability and efficiency of the intended neuronal responses to control a brain computer interface (BCI). Performing motor imagery tasks causes proper formation of special patterns at a specific timeframe of the EEG signal. The accurate selection of this optimal informative timeframe has not yet been investigated. Previous studies have considered an identic portion of data for all individuals, while neglecting that the duration and delay takes for the motor imagery brain activities to be well reflected in EEG signals vary between individuals. We propose an intelligent hybrid genetic algorithm-support vector machine (SVM) method to select the most stimulated timeframe of interest. The method also selects the most distinctive subset of features (through a comprehensive fused set of temporal, spectral and wavelet inspected information) while simultaneously optimize the SVM classifier's parameters. Evaluation results show that not only the most stimulated timeframe has a short duration but also occurs after a specific delay: that they are different between individuals. Using this optimal timeframe, the classification accuracy increased up to 92.14% for Graz 2003 and 89.00%, 84.81% and 85.00% for O3, S4 and X11 subjects of Graz 2005 database respectively. These results that were obtained despite the use of a small set of features confirm that this intelligent method can be effective in increasing the computational speed while decreasing the computational complexity which provides the potential capability of including in real time BCI systems.