The study presented in this paper shows that electrocorticographic (ECoG) signals can be classified for making use of a human brain-computer interface (BCI) field. The results show that certain invariant phase transition features can be reliably used to classify two types of imagined movements accurately. Those are the left small-finger and tongue movements. Our approach consists of two main parts: channel selection based on Tsallis entropy in Hilbert domain and the nonlinear classification of motor imagery with support vector machines (SVMs). The new approach, based on Hilbert and statistical/entropy measurements, were combined with SVMs based on admissible kernels for classification purposes. The classification accuracy rates were 95% (264/278) and 73% (73/100) for training and testing sets, respectively. The results support the use of classification methods for ECoG-based BCIs.