Thrust reverser for a jet engine

The thrust reverser comprises a fan duct (10) defined between an inner skin (21) and an outer skin (9) into which integrates the inner skin (5i) of a sliding cowl (3; 3') in the direct thrust situation, said outer skin (5i) of the fan duct (10) having a radius Re, in the plane (P'1), transverse to the longitudinal axis of the reverser and passing through the upstream end (23') of the sliding cowl in the direct thrust situation, and the inner skin (21) of the fan duct (10) presenting, downstream of this upstream plane (P'1), a maximum radius Ri in a plane (P2), parallel to the upstream plane (P'1). According to the invention, the radius Re is less than the radius Ri.