The invention relates to an unducted-fan aircraft engine comprising a generally cylindrical nacelle through which a primary jet flows, the nacelle bearing a fan rotor comprising variable-pitch vanes (33) located radially outside the nacelle in order to be traversed by a secondary jet (31) flowing longitudinally around the nacelle. The rotor comprises a hub bearing variable-pitch vane supports each carrying one vane (33), each vane (33) comprising a blade extending from a root that is used to removably attach same to a base of the associated support (34). Each base (36) is located radially outside the nacelle so that it is in the secondary jet, and each assembly formed by a base (36) and the vane root supported by the base (36) is surrounded and covered by a detachable aerodynamic cover (37).