Abstract In order to guarantee an unbiased solution in accelerometer measurements, calibration parameters have been finally calculated without using any kind of regularization or constraint. In this paper, a better calibration of the GRACE accelerometers is achieved from the instantaneous GPS-based non-gravitational accelerations. The first derivatives of the precise-orbit velocity are computed under an a priori arc-to-chord threshold, while the modelled time-varying forces of gravitational origin and reference-system rotations are computed according to current conventions (including sub-daily tide variations). After subtracting the modelled time-varying gravity from the GPS-based accelerations, cross-track axes of both GRACE satellites seem to be affected by a periodic error of unknown source. With the purpose of extracting the underlying information from the resulting data, the systematic error is modelled and subtracted successfully. According to this approach, the resulting accelerations serve as a reliable reference for accelerometer calibration.