A method for continuously annealing aluminum alloy sheet at final thickness by continuously moving heat-treatable AlMgSi aluminum alloy sheet through a continuous annealing furnace arranged to heat the moving aluminum sheet to a set soaking temperature (TSET) in the temperature range of 500° C. to 590° C., the continuous annealing furnace has an entry section and an exit section, the moving aluminum sheet moves substantially horizontally through the continuous annealing furnace, wherein the moving aluminum sheet is rapidly cooled on leaving the exit section, wherein before or near the entry section of the continuous annealing furnace the moving aluminum sheet is pre-heated to a temperature of 5° C. to 100° C. below the TSET using an average heat-up rate as function of sheet thickness of at least Y=−31·ln(X)+50, wherein Y is the heat-up rate in ° C./sec and X is the sheet thickness in mm.