A second-order phase transition of alpha2 form isotactic polypropylene (iPP) is found at high annealing temperature (T-a = 159.3 degreesC) by means of X-ray diffraction method. Although the lattice shape and the space group keep the same as those of the alpha2 form, i.e. monoclinic and P2(1)/c, with increase of T-a, it has been revealed that there are discontinuous increases in the slopes of the lattice constants a and b against T-a plots, while the c and the beta keep almost constant. As a result, the slope of the unit cell volume V versus T-a plot also shows a discontinuous increase at T-a = 159.3 degreesC, indicatin- the occurrence of the second-order phase transition. In order to distinguish the two phases, the phase above the transition temperature is named alpha2' phase and the transition temperature is denoted Talpha2-alpha2'. These facts suggested that the alpha2' form is a mobile phase where the molecular chains would become loosely packed and mobile, promoting the better chain sliding diffusion. A fast lamellar thickening process has been confirmed in the higher temperature region than Talpha2-alpha2', which was reported in the precedent paper. General significance is proposed that mobile phases possibly exist at high temperature, close to the melting temperature and accelerate lamellar thickening, which improves physical properties of polymers.