Method for operating an internal combustion engine with direct fuel injection

In a method of operating an internal combustion engine with direct fuel injection such that, in the engine startup period, a three-way catalytic converter disposed in the engine exhaust system is rapidly heated to a working temperature, in that a fuel quantity which is injected is injected in two separate injection steps with the first fuel volume being injected during the intake stroke and the second fuel volume being injected during the expansion stroke so as to form immediately before the ignition instant a rich stratified charge cloud in the region of the spark plug thereby ensuring reliable ignition of the stratified cloud while, overall, achieving a lean fuel/air mix in the combustion chamber.