This paper is to issue a new theorem in the field of the theory of adjustment for reflecting prisms:Theorem of Adjustment for Reflecting Prisms.First, an embryonic form of this theorem called the "cosine law and two-vector subtraction rule", referred only to the image lean has been discussed relatively in detail, although it was created by the author 40 years ago. And then its follow-on evolving process including five times of going up has been briefly described. Finally an exact and clear definition of the theorem is given.