  In the Dirac theory of the quantum-mechanical interaction of a magnetic
monopole and an electric charge, the vector potential is singular from the
origin to infinity along certain direction - the so called Dirac string.
Imposing the famous quantization condition, the singular string attached to the
monopole can be rotated arbitrarily by a gauge transformation, and hence is not
physically observable. By deriving its analytical expression and analyzing its
properties, we show that the gauge function $\chi({\bf r})$ which rotates the
string to another one has quite complicated behaviors depending on which side
from which the position variable ${\bf r}$ gets across the plane expanded by
the two strings. Consequently, some misunderstandings in the literature are
clarified.
