The design of optimal DMT transceivers for distorted channel with colored noise has been of great interest. Of particular interest is the class of block based DMT, where the transmitter and the receiver consist of constant matrices. Two types of block-based DMT transceivers will be considered: the DMT system with zero padding (ZP-DMT) and the DMT system with general prefix (GP-DMT). We will derive the bit allocation formula. For a given channel and channel noise spectrum, we will design the ISI-free optimal transceiver that minimizes the transmission power for a given transmission rate and probability of error. For both ZP-DMT and GP-DMT systems, the optimal ISI-free transceiver can be given in closed from. We will see that for both classes, the optimal transceiver has an orthogonal transmitter. Simulation shows that the optimal DMT system can achieve the same transmission rate and the same probability of error with a much lower transmission power compared with other existing DMT systems.