1. A method for correcting an electron energy loss spectral image acquired by a transmission electron microscope having an electron spectroscope, the method comprising steps of: acquiring a two-dimensional standard spectral image with a first axis representing the amount of an energy loss and a second axis representing positional information; comparing a spectrum extracted from the standard spectral image at a standard position with a spectrum extracted from the standard spectral image at each position other than the standard position and calculating correction information at each position based on a difference between the spectrum at the standard position and the spectrum at each position other than the standard position, the difference based on a zero loss spectral image or an electron energy loss spectral image acquired from a sample to be analyzed; acquiring an electron energy spectral image from the sample; correcting the spectrum of the spectral image from the sample at each position based on the correction information.