The traditional use of fixed apertures in determining the well known color-magnitude (CM) relation of early type galaxies, coupled with the presence of radial color gradients within these systems, introduces a bias in the CM relation itself. The effect of this bias is studied here deriving a CM relation which is based on color measurements carried out homogeneously within an aperture of radius equal to that of the galaxy effective radius. A sample of 48 giant early-type galaxies in the Coma cluster, with CCD observations in the U- and V-band, is used for this derivation. It is found that internal radial color gradients in early-type galaxies cannot be neglected when discussing the colors of these systems, and that the CM relation derived using color measurements within the effective radius is significantly flatter than those based on fixed-aperture color measurements. With the presently available data it is impossible to determine whether the relation is completely flat, or whether a small correlation is still present between galaxy color and luminosity.
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