The invention relates to the manufacture of a cold-rolled steel sheet having a strength of more than 900 MPa, an elastic limit of more than 700 MPa and distributed elongation of more than 12%, the composition of which includes, the contents being expressed as weight percentages: 0.26%≤C≤0.45%, 1.0%≤Mn≤3.0%, 1.0%≤Si≤3.0%, Al≤0.10%, 0%≤Cr≤1.5%, S≤0.005%, P≤0.020%, Nb≤0.1%, Ti≤0.020%, V≤0.015%, N≤0.01%, the remainder of the composition being iron and inevitable impurities resulting from the production process. The microstructure, given in surface proportions, comprises 13% to 25% residual austenite and 13% to 30% MA islands, the remainder consisting of bainite and possibly ferrite.