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.
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