The invention relates to a trailer coupling for a motor vehicle (200), comprising a coupling arm (11) for coupling a trailer (300) or a rear load carrier, comprising a vehicle holder (20) that is/can be secured to the motor vehicle (200) and has a mounting base (23), on which a coupling arm carrier (30) (on which the coupling arm (11) is arranged) is mounted such that it can swivel about at least one swivel axis (S) between a use position (G) provided for attaching the trailer (300) or the rear load carrier and a non-use position (N) provided for a non-use of the trailer coupling (10), in which the coupling arm (11) advantageously does not protrude as far in front of the motor vehicle (200) as in the use position (G) in the state in which it is mounted on the motor vehicle (200), wherein the trailer coupling (10) has a fixing device (60) for stationarily fixing the coupling arm (11) in the use position (G) and/or the non-use position (N) relative to the mounting base (23), wherein the coupling arm (11) can be moved between the use position (G) and the non-use position (N) in a release position (L) of the fixing device (60) relative to the mounting base (23), and same can be stationarily fixed in a fixing position (F) of the fixing device (60) relative to the mounting base (23), wherein the fixing device (60) has at least one fixing surface (311, 312) securely arranged on the mounting base (23) and at least one fixing surface (311, 312) securely arranged on the coupling arm carrier (30), and wherein the fixing surfaces (311, 312) are directly or indirectly supported on one another in the fixing position (F) of the fixing device (60) for the rotational fixing of the coupling arm carrier (30) relative to the mounting base (23). The trailer coupling comprises at least one adjusting device (310, 320) for adjusting a longitudinal position (L1, L2) and/or a radial position (R1, R2) of at least one of the fixing surfaces (311, 312) on the the coupling arm carrier (30) or the mounting base (23) relative to the swivel axis (S).