A method of supervising for a function for aiding the following of the traffic lane of a motor vehicle, comprising on the one hand means for detecting lateral lines (30, 32) traced on the ground on the two sides of this traffic lane, so as to deliver the nominal lateral positions of each line (Yri, Yle), and on the other hand sensors (40, 42) of the dynamics of the vehicle which deliver the longitudinal speed (Vx) and the rate of yaw (Ψ') of this vehicle, characterized in that it calculates on the basis of the nominal values of the angle of heading (Θ) and of the mean curvature of this traffic lane, the values estimated individually for each of these lateral lines, of curvature (Cest. ri, Cest. le), of angle of heading (Θest. ri, Θest. le), and of lateral position of this line (Yest. ri., Yest. le), implementing the following steps in parallel for each of the lines (30, 32): - it multiplies the longitudinal speed (Vx) by the curvature, then the result is compared to a first value originating from a return loop, the difference giving a second value; - it then divides this second value by the longitudinal speed (Vx), the result giving the estimated curvature (Cest.) of the line concerned; - the second value is compared with the rate of yaw (Ψ'), the difference giving a third value which is entered with the nominal angle of heading (Θ) in an operational amplifier, to obtain a fourth value which is the estimated angle of heading (Θest.) of the line concerned; - the fourth value is multiplied by the longitudinal speed (Vx) to obtain a fifth value, which is compared with a sixth value, the difference giving a seventh value; - the seventh value is then entered with the nominal position of the line concerned in an operational amplifier, to give the estimated position (Yest.) of this line; - the estimated position (Yest.) of the line concerned is compared to its nominal position, the difference giving an eighth value which is multiplied by a first gain to give the sixth value, in parallel the eighth value is multiplied by a second gain, to give a ninth value; - furthermore, the fourth value is compared with the nominal angle of heading (Θ), then the difference is multiplied by a third gain to give a tenth value; - the ninth and tenth value are finally added to give the first value of the return loop. - it multiplies the longitudinal speed (Vx) by the curvature, then the result is compared to a first value originating from a return loop, the difference giving a second value; - it then divides this second value by the longitudinal speed (Vx), the result giving the estimated curvature (Cest.) of the line concerned; - the second value is compared with the rate of yaw (Ψ'), the difference giving a third value which is entered with the nominal angle of heading (Θ) in an operational amplifier, to obtain a fourth value which is the estimated angle of heading (Θest.) of the line concerned; - the fourth value is multiplied by the longitudinal speed (Vx) to obtain a fifth value, which is compared with a sixth value, the difference giving a seventh value; - the seventh value is then entered with the nominal position of the line concerned in an operational amplifier, to give the estimated position (Yest.) of this line; - the estimated position (Yest.) of the line concerned is compared to its nominal position, the difference giving an eighth value which is multiplied by a first gain to give the sixth value, in parallel the eighth value is multiplied by a second gain, to give a ninth value; - furthermore, the fourth value is compared with the nominal angle of heading (Θ), then the difference is multiplied by a third gain to give a tenth value; - the ninth and tenth value are finally added to give the first value of the return loop.