Method and apparatus for reducing the convergence time of an echo canceller including a transversal filter having N adjustable complex coefficients comprises the following steps:transmitting a complex training signal constituted by data d(n) transmitted at instants nT, where T is the data interval, having a period LT at least equal to NT and having the following two properties: ##EQU1## for every integer i such that 1.ltoreq.i.ltoreq.N-1, and ##EQU2## for every integer i such that 0.ltoreq.i.ltoreq.N-1; after the transmission of N data, calculating the coefficients C of the transversal filter from the sequence formed by the next L data transmitted, in accordance with the expression: ##EQU3## where C.sub.o represents the N initial coefficients,e.sub.R (n) is the difference signal between the received signal and the real output signal of the transversal filter,D.sup.* (n) represents the complex conjugate value of the last N data entering the transversal filter, and.sigma..sup.2 is a constant characterizing the power of each of the transmitted data.