The clamping fixture comprises a chuck (1) and fixedly securable thereto releasably a clamping pallet (6). The chuck (1) is provided with four centering pins (3) arranged at the chuck (1) cooperating with centering openings (9) arranged at the clamping pallet (6) such that the clamping pallet (6) when chucked in the chuck (1) is oriented in the X and Y direction. Each centering pin (3) features two conically tapered side faces (3a, 3b) whilst each centering opening (9) is defined by two side walls (9a, 9b) oriented parallel to each other. When chucking the clamping pallet (6) at the chuck (1) the conically tapered side faces (3a, 3b) of each centering pin (3) come into line contact with the sidewalls of the centering opening (9).