Among the sample of red giant stars in the globular clusters M3 and M13 whose CN bands $(3883{AA})$ have been measured by various authors, the stars on the red giant evolutionary state are selected to have their CN band distributions. It is found that all stars brighter than Mv = 0, are CN-strong in M3, while all stars except IV-29 are CN-strong in M13. It hints that the onset of meridional mixing is related with the RGB bumps of the clusters.