We explore an adaptive transmultiplexer (TMUX) technique used for multicarrier communication systems and find the Wiener solution and adaptive reconstruction algorithm. In order to obtain good performance and low computational complexity, a fast recursive least squares (RLS) algorithm is developed. By using the polyphase decomposition method, the adaptive receiver in a filter bank system can be formulated as a multichannel filtering problem. Simulations show that the proposed algorithm, called the block step-up step-down (B-SUSD) algorithm, has the convergence rate close to the standard RLS algorithm. Finally, the new adaptive TMUX receiver is applied to the WLAN system compared to the conventional IEEE 802.11a OFDM system to show the superior performance for a filterbank-based muticarrier communication system.