A new system of multicarrier modulation is described, which takes advantage of the biorthogonality property, to generalize the oversampled OFDM technique into a biorthogonal frequency division multiplex scheme named BFDM/QAM. A discrete-time analysis of this scheme leads to a discrete model of modulated transmultiplexer. Using a polyphase decomposition of this transmultiplexer, and assuming a distortion free channel, we determine the mathematical conditions on the prototype filters, allowing an exact cancellation of intersymbol and interchannel interference, i.e. a perfect reconstruction. Then, computationally efficient realizations of the modulators and demodulators are given. Lastly, some design examples are provided.