1. A method of detecting the presence of a filamentary object ( 14 ) suspended in the field of view of a telemeter ( 11 ) on board an aircraft ( 10 ), the method comprising the following steps: i) calculating the terrestrial coordinates (x,y,z) of points corresponding to echoes (S,G,D) delivered by the telemeter, and selecting candidate points from said points; ii) searching in a horizontal plane for straight line segments that are close to vertical projections of the candidate points; and iii) searching in each vertical plane containing one of the straight line segments found in step ii) for portions of catenaries that are close to the candidate points; wherein in step iii), for each vertical plane under consideration, and for each triplet of candidate points close to the vertical plane under consideration, the method comprises calculating the values of three parameters a, b, and c of a catenary (of equation of the form y=a*cos h((x/a)+b)+c) containing the projections on the vertical plane of the three points of the triplet under consideration, and then determining the presence of at least one suspended filamentary object as a function of the distribution of values of catenary parameters calculated for all of the triplets of candidate points close to the vertical plane under consideration.