We re-examine the correlation between the colors and the inclinations of the Classical Kuiper Belt Objects (CKBOs) with an enlarged sample of optical measurements. The correlation is strong (rho=-0.7) and highly significant (>8 sigma) in the range 0-34 deg. Nonetheless, the optical colors are independent of inclination below ~12 deg, showing no evidence for a break at the reported boundary between the so-called dynamically "hot" and "cold" populations near ~5 deg. The commonly accepted parity between the dynamically cold CKBOs and the red CKBOs is observationally unsubstantiated, since the group of red CKBOs extends to higher inclinations. Our data suggest, however, the existence of a different color break. We find that the functional form of the color-inclination relation is most satisfactorily described by a non-linear and stepwise behavior with a color break at ~12 deg. Objects with inclinations >12 deg show bluish colors which are either weakly correlated with inclination or are simply homogeneously blue, whereas objects with inclinations <12 deg are homogeneously red.