A new ordered structure has been found in a ternary Mg-Cu-Si Laves phase whose composition is around Mg(Cu0.80Si0.20)2.50. The ordering between Cu and Si of Cl5-type Mg(Cu0.81Si0.19)2.53 specimen was analysed by a single crystal X-ray diffraction method. It belongs to a space group P41 32(or P4 332) having a=6.9598Å contrary to the disordered structure of Fd3m. The ordered structure is characterized by the ordered 4-fold screw arrangements of Cu and Si atoms located on four tetrahedra in the unit cell leaving Mg atoms on 8c sites. The order parameter S= αl−α2 was found to be 0.74 in this specimen, where αland α2 are occupancy factors of Cu for 12d and 4a sitesof the space group P4 132, respectively. The order parameters were measured as a function of annealing temperature by using Warren's method for quenched powder specimens of Mg(Cu 0.80 Si 0.20)2.40. The maximum value of S reached to 0.75 at 200°C, which is a little lower than the expected value of perfect order, S=0.85. The order parameter then decreases continuously with increasing annealed temperature and become zero at about 600°C, indicating order-disorder transformation temperature.