  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.
