A method of manufacturing a high Mn non-magnetic steel sheet having low permeability at a cryogenic temperature suitable for use in large scale particle accelerators, the method comprises rolling a steel material containing, on the wt % basis, from 0.05 to 0.18% of C, from 26.0 to 30.0% of Mn, from 5.0 to 10.0% of Cr, 0.05 to 0.15% of N and, optionally, from 0.50 to 5.0% of Ni, in which a rolling start temperature is from 1050 to 1200° C. and a rolling end temperature is from 700 to 1000° C. Further, a cold rolled sheet is annealed at an annealing temperature for cold rolled sheet of from 1050 to 1200° C. and cooled after annealing, the annealed sheet being preferably applied with temper rolling under control for the strength by varying a draft ratio.