A process of correction of the spectral inversion for a receiver in a digital communication system: the process allows the reception in the receiver of a training sequence presumably known according to a modulation of type π/2 BPSK or MDP2. The process includes the following steps: Demodulating of the training sequence; Calculating of the differential correlation on a set of N received samples (Rn) and presumably sent (Sn) to generate a result; Using the result to detect the beginning of the frame and to order a spectral inversion in the chain of reception of the aforementioned receiver before launching the detection of the beginning of the frame. A receiver to process automatically the spectral inversion is also described.