A method for producing a high strength steel sheet having a yield strength YS of at least 850 MPa, a tensile strength TS of at least 1180 MPa, a total elongation of at least 14% and a hole expansion ratio HER of at least 30%. The chemical composition of the steel contains: 0.15%≦C≦0.25%, 1.2%≦Si≦1.8%, 2%≦Mn≦2.4%, 0.1%≦Cr≦0.25%, Nb≦0.05%, Ti≦0.05%, Al≦0.50%, the remainder being Fe and unavoidable impurities. The sheet is annealed at an annealing temperature TA higher than Ac3 but less than 1000° C. for more than 30 s, by cooling it to a quenching temperature QT between 275° C. and 325° C., at a cooling speed sufficient to have, just after quenching, a structure consisting of austenite and at least 50% of martensite, the austenite content en.) being such that the final structure can contain between 3% and 15% of residual austenite and between 85 and 97% of the sum of martensite and bainite, without ferrite, heated to a partitioning temperature PT between 420° C. and 470° C. and maintained at this temperature for time between 50 s and 150 s and cooled to the room temperature.