1. A method for correcting an electron energy loss spectral image acquired by a transmission electron microscope having an electron spectroscope, comprising the steps of: acquiring a two-dimensional standard spectral image with an axis representing the amount of an energy loss and an axis representing positional information; comparing a spectrum extracted from a standard portion of the standard spectral image with a spectrum extracted from each measured portion that has positional information different from that of the standard portion and calculating correction information based on a difference between the spectrum extracted from the standard portion of the standard spectral image and the spectrum extracted from the measured portion; acquiring an electron energy spectral image from a sample to be analyzed; correcting a spectrum for each piece of the positional information included in the electron energy loss spectral image acquired from the sample to be analyzed based on the correction information calculated for each of the positional information.