This paper describes the polymorphism of the novel phase Bi(1-x)Ln(x)O(1.5) (Ln = Sm, Eu, Gd, Tb, and Dy with x=0.38, 0.375, 0.275-0.40, 0.275-0.35, and 0.30-0.35, respectively) which has a C-type rare-earth oxide-related structure. This C-type phase transformed without delay to the delta-Bi2O3 type high-temperature phase around 900 degrees C upon heating. Upon cooling, however, the delta-phase never returned to the original C-type phase. The irreversibility is only apparent, because the delta-phase transformed gradually to the C-type phase by annealing around 800 degrees C; in other words, the rate of transition from the delta to the C-type phase is extremely sluggish. The electrical conductivity of the C-type phase was not good (sigma=10(-3.9) S cm(-1) at 700 degrees C), though the oxide-ion transport number was 70% over a temperature range 600 to 850 degrees C.