A methodology for wavelet synthesis based on lifting scheme and genetic algorithms is presented. Often, the wavelet synthesis is addressed to solve the problem of choosing properly a wavelet function from an existing library, but which may be not specially designed to the application in hand. The task under consideration is the identification of epileptic seizures over electroencephalogram recordings. Although basic classifiers are employed, results rendered that the proposed methodology is successful in the considered study achieving similar classification rates that had been reported in literature.