The invention relates to a device for cancelling inter-symbol interference in a sampled digital signal. The device comprises a first filter, for which the optimum transfer function is identical to that of the transmission channel, and which receives a sequence of samples ({{tilde over (d)}.sub.n}.sub.n.epsilon.N) representative of the digital signal sent to the input of the transmission channel, a subtractor circuit to subtract the first filter output ({{tilde over (d)}'.sub.n}.sub.n.epsilon.N) from the sequence of input samples ({r.sub.n}.sub.n.epsilon.N), a second filter tuned to the transmission channel, with an optimum transfer function H*(f), to which the output ({e.sub.n}.sub.n.epsilon.N) from the subtractor circuit is input, and an adder circuit designed to add the output from the second filter to the sequence of samples ({{tilde over (d)}.sub.n}.sub.n.epsilon.N) representative of the digital signal sent to the input of the transmission channel, and thus generating a sequence of complex symbols ({.sub.n}.sub.n.epsilon.N) without any inter-symbol interference.