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Repetitive sequences of DNA are important to a number of regulatory functions; hence, to find repetitive DNA sequences is of considerable importance and worth to study. The purpose of this paper is to look for all possible repetitive sequences of DNA in a great deal and then to provide the biologists the repetitive sequences to do further work. Our approach first predicts the possible lengths of repetitive sequences based on the Fourier transform, and then proposes a so-called motif-identification algorithm (MIA) to find the repetitive patterns of the corresponding motif lengths. Our method compares favorably against some common motif-finding approaches, such as Spectral Repeat Finder and Gibbs sampler in all cases, and performs very well for the synthetic and real datasets.