CN and CH band strengths for ten new bright giants in the globular cluster M15 have been measured from archival spectra obtained with the Multiple Mirror Telescope. Using published indices for other bright M15 giants, a CN-CH band strength anticorrelation is found for bright red giants. However, stars that do not follow the CN-CH anticorrelation are also found. They seem to show a positive correlation between the two indices. Among them, all the AGB and HB stars of the sample are included. Stars I-38 and X6, which are located near the RGB fiducial line in the CMD, have low measured CH(G) indices compared with other RGB stars. Stars IV-38, S4, and S1, which are all near the RGB tip, have strong measured CH(G) indices. Therefore, most of their evolutionary states are suspected to be different from those of a normal single RGB star.