Abstract. A new algorithm approach called Weighting Function Differential Optical Absorption Spectroscopy (WFDOAS) is presented which has been developed to retrieve total ozone columns from nadir observations of the Global Ozone Monitoring Experiment. By fitting the vertically integrated ozone weighting function rather than ozone cross-section to the sun-normalized radiances, a direct retrieval of vertical column amounts is possible. The new WFDOAS approach takes into account the slant path wavelength modulation that is usually neglected in the standard DOAS approach using single airmass factors. This paper focuses on the algorithm description and error analysis, while in a companion paper by Weber et al. (2004) a detailed validation with groundbased measurements is presented. For the first time several auxiliary quantities directly derived from the GOME spectral range such as cloud-top-height and cloud fraction (O2-A band) and effective albedo using the Lambertian Equivalent Reflectivity (LER) near 377nm are used in combination as input to the ozone retrieval. In addition the varying ozone dependent contribution to the Raman correction in scattered light known as Ring effect has been included. The molecular ozone filling-in that is accounted for in the new algorithm has the largest contribution to the improved total ozone results from WFDOAS compared to the operational product. The precision of the total ozone retrieval is estimated to be better than 3% for solar zenith angles below 80°.