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In order to meet the requirements of online condition monitoring and automatic fault diagnosis of plants, the leakage errors of spectra in discrete spectrum analysis are corrected automatically. Aiming at the leakage errors in spectra of signals windowed by rectangular window, a automatic correcting method of leakage errors is presented based on the extremum searching method(ESM) and the energy centrobaric correction method(ECCM). The steps of the method are: firstly, compute the Discrete Fourier Transform (DFT) of the signal by Fast Fourier Transform (FFT) method and get the amplitude spectrum of it; secondly, find the all points needed to be corrected by the extremum searching method; thirdly, correct the frequencies, amplitudes and phases of the corresponding points by energy centrobaric correction method; finally, get the corrected signal by Inverse Fast Fourier Transform (IFFT) method. The simulation results certify that the leakage errors of spectra after being corrected can be controlled within 3% when the minimal difference in neighbouring frequency components is greater than 10 times of the frequency resolution. This correcting method can meet the requirements of engineering practice.