A method for estimating directions of arrival of incidence sources on an array comprising N narrowband antennae each receiving the contributions of P sources, the observations received on each antenna generating statistics that can be in the form of a 2q order cumulants matrix, with q>1, the coefficients of which are the circular 2 q order cumulants, Cum[x i 1 (t),..., x i q (t), x i q+1 ( t)*,..., x i 2q ( t)*], characterised in that it comprises at least the following steps: - ranking the 2q order statistics of the observations in order to obtain a rectangular 2q order matrix C 2 q, x v l of size (N v x N 2q- v), the coefficients of which are the circular 2q order cumulants of the observations, the ranking being carried out as follows: decomposing a 2 q -tuple, ( i 1,..., i q, i q +1,..., i 2 q), of indexes i j (1 ≤ j ≤ 2 q) (1 ≤ i j ≤ N), into a v-tuple and a (2 q-v)-tuple, respectively indexed by v and l, and respectively defined by ( i 1, i 2,..., i l, i q +1,..., i q + v-l) and ( i q + v + l,..., i 2 q, i l +1,..., i q) where the N V values of the v- tuple and the N 2q-v values of the (2 q-v)-tuple are denoted by integers I v,l and J v,l, such that 1 ≤ I v, l ≤ N v and 1 ≤ J v,l ≤ N 2 q-v, I v, l ≜ ∑ j = 1 l N v − 1 i j − 1 + ∑ j = 1 v − l N v − l − j i q + j − 1 + 1 I v, l ≜ ∑ j = 1 q − v + l N 2 q − v − 1 i q + v − l + j − 1 + ∑ j = 1 q − l N q − l − j i l + j − 1 + 1 - using an invariance property by permutating cumulants and deducing therefrom that: Cum x i 1 t,..., x i q t, x i q + 1 t *,..., x i 2 q t * = Cum [ x i 1 t,..., x i l t, x i q + 1 t *,..., x i q + v − l t *, x i q + v − l + 1 t *,..., x i 2 q t *, x i l + 1 t,.., x i q t], - then considering the preceding element to be the element [ I v,l, J v,l] of the rectangular matrix of the cumulants; - estimating the values of the directions using a goniometry algorithm applied to the estimated rectangular matrix. - ranking the 2q order statistics of the observations in order to obtain a rectangular 2q order matrix C 2 q, x v l of size (N v x N 2q- v), the coefficients of which are the circular 2q order cumulants of the observations, the ranking being carried out as follows: decomposing a 2 q -tuple, ( i 1,..., i q, i q +1,..., i 2 q), of indexes i j (1 ≤ j ≤ 2 q) (1 ≤ i j ≤ N), into a v-tuple and a (2 q-v)-tuple, respectively indexed by v and l, and respectively defined by ( i 1, i 2,..., i l, i q +1,..., i q + v-l) and ( i q + v + l,..., i 2 q, i l +1,..., i q) where the N V values of the v- tuple and the N 2q-v values of the (2 q-v)-tuple are denoted by integers I v,l and J v,l, such that 1 ≤ I v, l ≤ N v and 1 ≤ J v,l ≤ N 2 q-v, I v, l ≜ ∑ j = 1 l N v − 1 i j − 1 + ∑ j = 1 v − l N v − l − j i q + j − 1 + 1 I v, l ≜ ∑ j = 1 q − v + l N 2 q − v − 1 i q + v − l + j − 1 + ∑ j = 1 q − l N q − l − j i l + j − 1 + 1 decomposing a 2 q -tuple, ( i 1,..., i q, i q +1,..., i 2 q), of indexes i j (1 ≤ j ≤ 2 q) (1 ≤ i j ≤ N), into a v-tuple and a (2 q-v)-tuple, respectively indexed by v and l, and respectively defined by ( i 1, i 2,..., i l, i q +1,..., i q + v-l) and ( i q + v + l,..., i 2 q, i l +1,..., i q) where the N V values of the v- tuple and the N 2q-v values of the (2 q-v)-tuple are denoted by integers I v,l and J v,l, such that 1 ≤ I v, l ≤ N v and 1 ≤ J v,l ≤ N 2 q-v, I v, l ≜ ∑ j = 1 l N v − 1 i j − 1 + ∑ j = 1 v − l N v − l − j i q + j − 1 + 1 I v, l ≜ ∑ j = 1 q − v + l N 2 q − v − 1 i q + v − l + j − 1 + ∑ j = 1 q − l N q − l − j i l + j − 1 + 1 - using an invariance property by permutating cumulants and deducing therefrom that: Cum x i 1 t,..., x i q t, x i q + 1 t *,..., x i 2 q t * = Cum [ x i 1 t,..., x i l t, x i q + 1 t *,..., x i q + v − l t *, x i q + v − l + 1 t *,..., x i 2 q t *, x i l + 1 t,.., x i q t], - then considering the preceding element to be the element [ I v,l, J v,l] of the rectangular matrix of the cumulants; - estimating the values of the directions using a goniometry algorithm applied to the estimated rectangular matrix.