Digital transmission using existing amplitude modulation transmitters (AM) results in transmissions in undesired boundary zones. This results from the fact that the two signals, the A signal and the RF-P signal, formed from the digital modulation signal (I/Q signal), which are required for controlling the AM transmitter have bandwidths much larger than the separate branches, namely the A branch and the RF branch, and said two signals enter with a propagation time difference in the multiplier of the transmitter output stage. Known methods for equalizing propagation time, up to at least 0.3 microseconds, and for reducing bandwidth, for example by a hole in the vectogram of the I/Q signal around the point 0/0, do not allow to reduce sufficiently transmissions in boundary zones. The method, in accordance with the present invention, is based on the fact that the use of an adapted filter for the phase modulated RF-P signal enables to reduce distortions occurring as a result of band limitation and that transmissions in boundary zones can therefore be likewise reduced. The adapted filter is a Gaussian filter with linear phase route. But if it is directly introduced in the transmitter output stage, the filtered RF-P signal does not enable achievement of the objective since the amplitude variations would once more be interrupted as a result of the switched mode. Therefore the amplitude variations are detected by the derived RF-P signal after passing through the filter by an envelope phase detector and introduced as correction signal with the A signal in a multiplier used as an auxiliary in the A branch. The corrected A signal is then multiplied with the RF-P signal in the transmitter output stage.