Context. A recent analysis of IBEX measurements of the neutral interstellar He flux showed that the inflow velocity vector is different from the results of an earlier analysis of observations from the GAS instrument onboard Ulysses. A recently published compilation of published results on the helium inflow direction from the past ∼40 years suggested that the inflow direction may be changing with time. Aims. We reanalyzed the old Ulysses data and reprocessed them to increase the accuracy of the instrument pointing to investigate whether the GAS/Ulysses observations, carried out during almost two solar cycles, support the hypothesis that the direction of the interstellar helium inflow is changing. Methods. We employed a similar analysis method as had been used in the analysis of the IBEX data. We sought a parameter set that minimizes the reduced χ 2 , using the Warsaw test-particle model for the interstellar He flux at Ulysses with a state-of-the-art model of neutral He ionization in the heliosphere that precisely reproduces the observation conditions. We also propose a supplementary method of constraining the parameters based on cross-correlations of parameters obtained from an analysis of carefully selected subsets of data. Results. We find that the ecliptic longitude and speed of interstellar He agree very well with the values reported in the original GAS analysis. We find, however, that the temperature is markedly higher. The three-seasons best-fit parameter set is λ = 255.3 • , β = 6 • (J2000), v = 26.0 km s −1 , and T = 7500 K. We do not find evidence that these parameters are varying with time, but their uncertainty range is wider than originally reported. Conclusions. The originally derived parameters of interstellar He from direct sampling on GAS/Ulysses agree well with those currently derived, except for the temperature, which seems to be appreciably higher; this agrees well with interstellar absorption line results. While the results of our analysis agree marginally with the previously reported results from IBEX, the most likely values from the two analyses differ for reasons that are still not understood.