Method for correcting the richness of an air and fuel mixture supplying an internal combustion engine in the period between starting the engine and reaching the operating temperature of an oxygen sensor positioned in an exhaust line of the engine, in which: - is determined, and from this setpoint (Cr) a quantity of fuel to be injected into the internal combustion engine, - when starting the engine, a temperature representative of the thermal state of the engine is measured, - the oxygen sensor is heated, - is calculated and the process is activated if this time is greater than an engine stop time threshold. determined for which the engine is considered to be sufficiently cooled, and if the process is activated, - we determine according to the value of this representative temperature of the thermal state of the engine, a corrective factor (Fcr) to be applied to the quantity of fuel to be injected determined from the richness setpoint (Cr) and we apply this factor corrective factor (Fcr) until the oxygen sensor has reached its operating temperature, the corrective factor (Fcr) being determined from a map establishing this factor as a function of the temperature representative of the thermal state of the engine, characterized in that: - the temperature representative of the thermal state of the engine measured during start-up is stored, - we measure the time elapsed between the start of the startup and the probe reaching oxygen from its operating temperature, and when the oxygen sensor has reached its operating temperature, - is determined from the difference between the richness setpoint (Cr) and the richness determined from the measurement of the oxygen sensor, - replaced by this current corrective factor, the replacement of the corrective factor (Fcr) being authorized only if the time elapsed between the start of the startup and the probe reaching oxygen of its operating temperature is greater than a threshold of duration of operation of the oxygen sensor. - is determined, and from this setpoint (Cr) a quantity of fuel to be injected into the internal combustion engine, - when starting the engine, a temperature representative of the thermal state of the engine is measured, - the oxygen sensor is heated, - is calculated and the process is activated if this time is greater than an engine stop time threshold. determined for which the engine is considered to be sufficiently cooled, and if the process is activated, - we determine according to the value of this representative temperature of the thermal state of the engine, a corrective factor (Fcr) to be applied to the quantity of fuel to be injected determined from the richness setpoint (Cr) and we apply this factor corrective factor (Fcr) until the oxygen sensor has reached its operating temperature, the corrective factor (Fcr) being determined from a map establishing this factor as a function of the temperature representative of the thermal state of the engine, - we determine according to the value of this representative temperature of the thermal state of the engine, a corrective factor (Fcr) to be applied to the quantity of fuel to be injected determined from the richness setpoint (Cr) and we apply this factor corrective factor (Fcr) until the oxygen sensor has reached its operating temperature, the corrective factor (Fcr) being determined from a map establishing this factor as a function of the temperature representative of the thermal state of the engine, characterized in that: - the temperature representative of the thermal state of the engine measured during start-up is stored, - we measure the time elapsed between the start of the startup and the probe reaching - the temperature representative of the thermal state of the engine measured during start-up is stored, - we measure the time elapsed between the start of the startup and the probe reaching oxygen from its operating temperature, and when the oxygen sensor has reached its operating temperature, - is determined from the difference between the richness setpoint (Cr) and the richness determined from the measurement of the oxygen sensor, - replaced by this current corrective factor, the replacement of the corrective factor (Fcr) being authorized only if the time elapsed between the start of the startup and the probe reaching oxygen of its operating temperature is greater than a threshold of duration of operation of the oxygen sensor. - is determined from the difference between the richness setpoint (Cr) and the richness determined from the measurement of the oxygen sensor, - replaced by this current corrective factor, the replacement of the corrective factor (Fcr) being authorized only if the time elapsed between the start of the startup and the probe reaching oxygen of its operating temperature is greater than a threshold of duration of operation of the oxygen sensor.