The molecular replacement method consists of the three consecutive stages : (1) determination of the orientation of the molecule in the crystal, (2) determination of the position of the molecule and (3) solution of the phase problem.The problem in the first stage was solved almost satisfactorily by using the rotation function first developed by Rossmann and Blow and recently improved by Crowther.In the second stage, the problem was not always solved satisfactorily because of several theoretical and/or computational drawbacks inherent to the translation function.Lack of efficient translation functions of universal applicability prevented the po-tentially much more powerful molecular replacement method from being popular in the structure determinations of macromolecules.A case of a known model structure is discussed, considering the origins of inefficacy of the translation functions proposed so far, and a new powerful translation function which is highly efficient in computation is proposed.