We here present a new computationally efficient method of computing the luminosity function of galaxies. Determination of the luminosity function is necessary to remove selection effects in the Sloan Digital Sky Survey (SDSS) data so that scientists may analyze intergalactic structures and assess the validity of claims of galacto-centric shells. The new method is expected to give a more accurate determination of the luminosity and selection functions than other methods. We apply this method to data from the SDSS and find that the results are consistent with older, traditional methods, and yet of higher quality for low-brightness galaxies. We find that small variations in galaxy density as a function of redshift do exist, and are not due to the Malmquist bias.