In certain problems of X-ray crystallography it became necessary to determine the coordinates of a point P, originally at (x, y, z) in the non-rectangular, Cartesian system (X, Y, Z) after rotation of the vector about some line . This is the classical Euler transformation, and the result is well known for rectangular axes. Since, however, no reference could be found to the more general case, the results of this calculation may be of interest.