We report on improvements to the sulfur extraction method out of silicate glasses by the use of HF + CrCl2 solution for the precise determination of S multi-isotope compositions. This protocol has been designed to be sulfide specific and if needed, can be easily extended to oxidized sulfur. The complete method was validated on a synthetic powder and three laboratory mid-ocean ridge glassy internal standards (CH98 DR12, ED DR46 1-6 and ED DR26 type 1). S extraction yields of the three basalt glass standards were 100 ± 4% (1σ, n = 12), 102 ± 6% (1σ, n = 4) and 97 ± 6% (1σ, n = 4) respectively. Their δ34S show little variation, at − 1.20 ± 0.08‰, − 1.09 ± 0.14‰ and − 1.25 ± 0.12‰ (all 1σ) with respect to V-CDT. Δ33S and Δ36S are both negative with respect to our SF6 tank, between − 0.018 and − 0.021‰ (± 0.012‰ maximum 1σ) for Δ33S and between − 0.216 and − 0.282 (± 0.106 maximum 1σ) for Δ36S. The method was then applied to sixteen additional glasses from worldwide mid-ocean ridges, including three samples for which δ34S was reported previously. Our results show that previous data are affected by a systematic δ34S shift toward positive values, of ≃ 0.4 to 1.5‰. We infer that this shift originates from an incomplete S recovery when the Kiba extraction protocol is used. δ34S values range between − 1.80 and 0.02‰ with a mean value of − 0.91 ± 0.50‰ (1σ n = 19). Such negative values contrast with the positive range previously reported leading us to suggest a revised mantle δ34S, mainly dominated by negative values. Δ33S and Δ36S are strikingly homogeneous with mean respective values of − 0.019 ± 0.005‰ and − 0.193 ± 0.093‰ (1σ n = 19) versus our SF6 tank. These estimates are indistinguishable from our CDT measurements and define the best present-day upper mantle estimate.