Using three volume-limited samples of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we have investigated how other properties of galaxies depend on the environment at fixed luminosity. At fixed luminosity, we still observe strong environmental dependence of g - r color, concentration index, and morphology of galaxies: red, highly concentrated, and early type galaxies exist preferentially in the densest regions of the universe, while blue, poorly concentrated, and late type galaxies are located preferentially in low density regions. This shows that luminosity is not fundamental in correlations between galaxy properties and the environment.