Satellite radar altimetry has been providing estimates of global mean sea level (GMSL) since 1992. The early TOPEX record originates from two identical instruments, which requires the estimation of an intermission bias and careful handling of the problematic first part of the record. Calibration of TOPEX is crucial to obtain a continuous and consistent record, which is needed to quantify any recent acceleration. We propose a novel approach to calibrate TOPEX altimeter data using sea surface height differences at crossovers of TOPEX and ERS. Tide gauges are only used to determine a drift in one of the two datasets. We provide a new and more accurate estimate of the intra-mission bias, which leads to a much reduced GMSL acceleration over the whole record. Hence, the conundrum of an uncertain GMSL acceleration from altimetry is still unsolved, in spite of recent opposite claims, and in contrast to the expected effect of ocean warming and continental freshwater fluxes.