A hot-rolled austenitic iron/carbon/manganese steel sheet, the strength of which is greater than 1200 MPa, the product P (strength (in MPa)×elongation at break (in %)) of which is greater than 65 000 MPa % and the nominal chemical composition of which comprises, the contents being expressed by weight: 0.85%≦C≦1.05%; 16%≦Mn≦19%; Si≦2%; Al≦0.050%; S≦0.030%; P≦0.050%; N≦0.1%, and, optionally, one or more elements chosen from: Cr≦1%; Mo≦0.40%; Ni≦1%; Cu≦5%; Ti≦0.50%; Nb≦0.50%; V≦0.50%, the rest of the composition consisting of iron and inevitable impurities resulting from the smelting, the recrystallized surface fraction of said steel being equal to 100%, the surface fraction of precipitated carbides of said steel being equal to 0% and the mean grain size of said steel being less than or equal to 10 microns.