Abstract: For many years, the fractional Fourier Transform (FRFT) is deep investigated because of a generalization of the conventional Fourier transform The engineering realization of the continuous FRFT has to be sampled and discretized, and such an achieved core matrix will lose many important properties. Thus, people have done many researches on the discrete realization of the core matrix of the continuous FRFT. In this paper, a newly commuting matrix is proposed to implement the discrete fractional transform (DFRFT). The core matrix of the DFRFT resulted from the presented commuting matrix has the similar properties with the core of the continuous fractional Fourier transform, such as unitary, additive, orthogonal, reversible. Finally, the simulation results have shown the similarity of the core matrix of the proposed DFRFT and the core function of continuous FRFT, and the similarity of two FRFTs of rectangular signal