Abstract: Method of high-resolution direction finding to an arbitrary even order, 2q (q>2), for an array comprising N narrowband antennas each receiving the contribution from P sources characterized in that the algebraic properties of a matrix of cumulants of order 2q, C2q,x(l), whose coefficients are the circular cumulants of order 2q, Cum[xi1(t), . . . , xiq(t), xiq+1(t)*, . . . , xi2q(t)*], of the observations received on each antenna, for cumulant rankings indexed by l, are utilized to define a signal subspace and a noise subspace.