As a new method for discrimination analysis applicable to data containing a large number of variables such as spectra, FDOD (Fisher's Discriminant Orthogonal Decomposition) was developed by incorporating regularization and orthogonal decomposition into ordinary FDA (Fisher's Discriminant Analysis). Here, FDOD was applied to distinguish infrared absorption (IR) spectra of rayon and modal. Since rayon and modal are very similar recycled fibers, their IR spectra cannot be discriminated by score plots based on principle component analysis (PCA). By using FDOD, their discrimination with a correct answer rate of 94% has been achieved.