In this work, the design of filter bank multicarrier (FBMC) sytems using several kinds of Modified Discrete Fourier Transform (MDFT) filter banks is considered. Our attention is focused on Nearly Perfect Reconstruction (NPR) systems since an increase of selectivity and discrimination in each subchannel filter can provide better performance than the equivalent perfect reconstruction system. A new scheme is proposed with the main novelty of embedding an MDFT FBMC system into the standardized DFT-based multicarrier modulator (MCM). The new system also inserts a cyclic prefix into each transmitted symbol to facilitate the equalization task at the receiver. Finally, in order to illustrate the properties and capabilities of the proposed system, several simulation results are presented. They show that the proposed system can improve the standard DFT-based MCM.