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Satellite altimetry missions now provide more than 25 years of accurate, continuous and quasi-global measurements of sea level along the reference ground track of TOPEX/Poseidon. These measurements are used by different groups to build the Global Mean Sea Level (GMSL) record, an essential climate change indicator. Estimating a realistic uncertainty in the GMSL record is of crucial importance for climate studies, such as assessing precisely the current rate and acceleration of sea level, analysing the closure of the sea-level budget, understanding the causes of sea-level rise, detecting and attributing the response of sea level to anthropogenic activity, or calculating the Earth's energy imbalance. Previous authors have estimated the uncertainty in the GMSL trend over the period 1993-2014 by thoroughly analysing the error budget of the satellite altimeters and have shown that it amounts to +/- 0.5 mm yr(-1) (90 % confidence level). In this study, we extend our previous results, providing a comprehensive description of the uncertainties in the satellite GMSL record. We analysed 25 years of satellite altimetry data and provided for the first time the error variance-covariance matrix for the GMSL record with a time resolution of 10 days. Three types of errors have been modelled (drifts, biases, noises) and combined together to derive a realistic estimate of the GMSL error variancecovariance matrix. From the latter, we derived a 90 % confidence envelope of the GMSL record on a 10 d basis. Then we used a least squared approach and the error variance-covariance matrix to assess the GMSL trend and acceleration uncertainties over any 5-year time periods and longer in between October 1992 and December 2017. Over 1993-2017, we have found a GMSL trend of 3.35 +/- 0.4 mm yr(-1) within a 90 % confidence level (CL) and a GMSL acceleration of 0.12 +/- 0.07 mm yr(-2) (90 % CL). This is in agreement (within error bars) with previous studies.