We present a new polarization correction algorithm for polarization sensitive spaceborne spectrometers like Global Ozone Monitoring Experiment (GOME) or Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY). These instruments measure polarization with less spectral resolution than the radiance. As a consequence, the current GOME polarization correction algorithm allows radiance errors of 10% in the UV and 3% in the visible (VIS) and near-IR. Using simulated spectra, we show that the continuum Stokes elements Q and U over a large wavelength range (300 to 800 nm) can be reliably retrieved from only a limited set of measurements (three to five). The interpolation to other wavelengths is made using numerically calculated polarization spectra. These polarization spectra can be calculated for Rayleigh scattering atmospheres, but we show that the retrieval is just as effective for cloudy and aerosol scenes as for clear scenes. For GOME the remaining radiance errors are less than 3% (UV) and 1% (VIS, near-IR), and often smaller than 0.5%. The lack of actual UV (300--330 nm) polarization measurements prevents further reduction of the radiance errors. We also show how the ozone Huggins absorption band may be accounted for through a parameterization and a single polarization broadband measurement and that strong but narrow absorption bands like the O2A band maybe ignored without detrimental effect on the algorithm.