We have investigated the quadruple sulfur isotopic composition of inorganic sulfur-bearing phases from 13 carbonaceous chondrites of CM type. We extracted sulfur from sulfides, sulfates, and elemental sulfur (S0) from all samples. We report mass independent signatures that are significantly larger than previously observed. We suggest that these mass independent S isotopic compositions record H2S photodissociation in the nebula. We present a model that ties aqueous alteration on chondrites with sulfur chemistry. This explains the transfer of mass independent signatures, produced in the gas phase of the nebula, to solid phases. If the model is correct, one can speculate that the occurence of S isotope mass independent signatures could be fingerprints of water accretion in these bodies.