In this paper CMOD5, a new C-band geophysical model function (GMF), is derived on the basis of measurements from the scatterometer on board of the European Remote Sensing Satellite ERS-2. First-guess winds from the European Centre for Medium-Range Weather Forecasts were used as a reference for the period from August to December 1998, adding up to more than 22,000,000 collocations. CMOD5 corrects some deficiencies of the currently widely used CMOD4 GMF. Linear and higher-order wind speed corrections as computed with a triple collocation method are implemented. Recent measurements of extreme backscatter and wind obtained by aircraft and in situ data are fitted. Also, a more accurate fit of the two-dimensional cone surface in three-dimensional measurement space is established, especially in the regime of strong winds. These improvements result not only in better wind retrievals at high wind speed, but also in a more uniform performance across the ERS scatterometer swath. Moreover, the wind ambiguity problem has been reduced owing to the improved fit of the cone surface, resulting in about 75% skill of the first rank solution for winds above 10 m/s. These improvements aid the general usefulness of retrieved C-band scatterometer winds for climate and weather applications, and the ambiguity removal in dynamical and extreme weather conditions in particular.