Triphenyl phosphite was studied by powder X-ray diffractometry, adiabatic calorimetry, and dielectric relaxation measurements. The highly correlated liquid, denoted by L-C, phase corresponding with the glacial phase by Cohen et al. was prepared by annealing the ordinary liquid, denoted by L-N, at 210 K, and different states in the L-C phase were formed by further annealing the prepared L-C-phase sample at 215 and 220 K. After the temperature jump from 210 to 215 K, two different processes first of heat absorption and then heat: evolution were found to exist in the L-C phase. The first process showed reversible temperature dependence of the relaxation times near the temperature of L-C-phase formation as far as the process bringing the latter heat evolution effect did not proceed any further. The glass transition temperatures were found to be 209.9, 212.6, and 214.0 K for the L-C-phase samples formed at 210, 215, and 220 K, respectively. The fragility parameters of the respective samples were 104, 99, and 94, comparable with 104 in the L-N phase. The second process changed the relaxation times of the first process irreversibly to increase as the temperature of L-C-phase formation increases in the order of 210, 215, and 220 K. The temperature dependences of beta-relaxation times were found to coincide completely with each other between the L-N and L-C phases. Those results were interpreted by the "intracluster rearrangement for alpha process" model combined with the "cluster structure for supercooled liquid and glass" model; the above second process corresponds to the increase/decrease in the size of the somehow "structurally ordered" region (named a cluster) and the first one to the order/disorder process of molecules within each cluster, namely the ordinary or process. The above second effect of heat evolution at 215 K is thus due to the development of ordering following the increase in the cluster size. The beta relaxation would be attributed to the rearrangement of molecules between the clusters.