In the general case of a Karle-Hauptman matrix containing no symmetry
equivalent reflections, maximizing the determinant as a function of th
e phases does not necessarily lead to an unambiguous solution of the p
hase problem. Individual phases may be shifted from their correct valu
es in a seemingly completely arbitrary way. This problem is discussed
in simple mathematical terms and a method is proposed allowing the ide
ntification of those elements in a Karle-Hauptman matrix possibly suff
ering from the effects discussed, given the space-group symmetry and t
he composition of the matrix. The conclusion reached in this paper is
that only the presence of a sufficiently large number of symmetry equi
valent reflections and/or Friedel opposites in a Karle-Hauptman matrix
causes the Generalized Maximum Determinant Rule to be an effective to
ol in ab initio phase determination.