  On the basis of the phase states, we present the correct integral expressions
of the two number-phase Wigner functions discovered so far. These correct forms
are derived from those defined in the extended Fock space with negative number
states. The analogous conditions to Wigner's original ones cannot lead to the
number-phase function uniquely. To show this fact explicitly, we propose
another function satisfying all these conditions. It is also shown that the
ununiqueness of the number-phase Wigner function result from the
phase-periodicity problem.
