Psychological bias towards, or away from, prior measurements or theory predictions is an intrinsic threat to any data analysis. While various methods can be used to try to avoid such a bias, e.g. actively avoiding looking at the result, only data blinding is a traceable and trustworthy method that can circumvent the bias and convince a public audience that there is not even an accidental psychological bias. Data blinding is nowadays a standard practice in particle physics, but it is particularly difficult for experiments searching for the neutron electric dipole moment (nEDM), as several cross measurements, in particular of the magnetic field, create a self-consistent network into which it is hard to inject a false signal. We present an algorithm that modifies the data without influencing the experiment. Results of an automated analysis of the data are used to change the recorded spin state of a few neutrons within each measurement cycle. The flexible algorithm may be applied twice (or more) to the data, thus providing the option of sequentially applying various blinding offsets for separate analysis steps with independent teams. The subtle manner in which the data are modified allows one subsequently to adjust the algorithm and to produce a re-blinded data set without revealing the initial blinding offset. The method was designed for the 2015/2016 measurement campaign of the nEDM experiment at the Paul Scherrer Institute. However, it can be re-used with minor modification for the follow-up experiment n2EDM, and may be suitable for comparable projects elsewhere.