The invention concerns a thrust reverser for a jet engine, of the type having swing doors (6) pivoting about fixed transverse pivots (7) secured to the rear end of flanges extending in line with pipe of the engine. According to the invention, each door (6) is borne by a connecting piece (10) offset towards the front with respect to a transverse plane passing through the pivot axis and orthogonal to the longitudinal axis of the door. Furthermore, the fairing (4a, 4b) extends as far as the rear end of the flanges, the said fairing and each door (6) being arranged, on the one hand, so as to cover completely the flanges in the folded position of the said door, and, on the other hand, to enable each door (6) to be brought into its deployed position without any interference between the said fairing and door.
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