A method for performing a precoding based on a generalized phase shift or a precoding based on an extended phase shift in a Multi-Input Multi-Output (MIMO) system employing several sub-carriers, and a transceiver for supporting the same are disclosed. A phase-shift-based precoding matrix is generalized by multiplying a diagonal matrix for a phase shift by a unitary matrix for maintaining orthogonality between sub-carriers. In this case, a diagonal matrix part may be extended by multiplying a precoding matrix for removing an interference between sub-carriers by a diagonal matrix for a phase shift. By generalization and extension of the phase-shift-based precoding, a transceiver is more simplified, and a communication efficiency increases.