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In this contribution we propose a new way to state and solve the channel equalization problem for an OFDM (Orthogonal Frequency Division Multiplexing) system, without the use of a guard interval. Therefore, the spectral efficiency is increased. The approach is based on the channel representation as a polynomial matrix. We develop a new decomposition of this matrix, which diagonalizes the channel matrix independently of the channel realization. It leads to a simple inversion of the channel matrix. The decomposition consists of forward and inverse DFTs and polynomial diagonal matrices. Further on, there is no restriction on the length of the channel impulse response