A new method is developed in which a circular dichroism (CD) spectrum is analyzed directly as a linear combination of the CD spectra (from 190 to 240 nm) of 16 proteins whose secondary structures are known from X-ray crystallography. This avoids the dilemma encountered in previous methods of trying to define single reference CD spectra that were supposed to characterize such broad and variable classes as helix, beta sheet, beta turn, and "remainder". It also permits a more accurate and flexible analysis. The usual instability in using so many parameters is automatically controlled by a simple constrained statistical regularization procedure (similar to ridge regression). Sixteen tests were made by removing 1 spectrum at a time from the set of 16 and analyzing it in terms of the other 15. The product moment correlation coefficients between the computed fractions of helix, beta sheet, beta turn, and remainder and the fractions from the X-ray data were 0.96, 0.94, 0.31,, and 0.49, respectively. Thus, the helix and beta-sheet accuracy is very good. (The corresponding values calculated by a previous method with four reference spectra were 0.85, 0.25, --0.31, and 0.46.).