The invention concerns a method for jointly decoding and equalizing a digital signal protected by a trellis-defined code and transmitted though a channel. The method consists in carrying out a maximum likelihood estimate of each current bit x_n by minimizing the quadratic error between the observed symbol V_n and the current symbol in the channel output z_n, the quadratic error being calculated (1002) from the set of observed symbols based on the branch metric of the last transition e_n1(X)e_n(X) according to the relationship (I); wherein k represents the rank of the coefficients of transverse filtering introduced by the radioelectric channel. The branch metric is calculated by backtracking through the successive states and the error propagating process is inhibited (1003) while backtracking through the successive states by storing at each node S survivors and by updating each survivor at the next time. The final survivor of the least metric is determined (1004) and the sequence of bits is read by backtracking through the successive nodes. The invention is applicable to ATM radio transmission.