  By exploiting the underlying symmetries of the relative phases of the
pseudoscalar meson photoproduction amplitude, we determine all the possible
sets of four double-spin observables that resolve the phase ambiguity of the
amplitude in transversity basis up to an overall phase. The present results
corroborate the original findings by Chiang and Tabakin [Phys. Rev. C 55, 2054
(1997)]. However, it is found that the completeness condition of four
double-spin observables to resolve the phase ambiguity holds only when the
relative phases do not meet the condition of equal magnitudes. In situations
where this condition occurs, it is shown that one needs extra chosen
observables, resulting in the minimum number of observables required to resolve
the phase ambiguity to reach up to eight, depending on the particular set of
four double-spin observables considered. Furthermore, a way of gauging when the
condition of equal magnitudes occurs is provided.
