Via analysis of spatiotemporal arrangements of atoms based on their dynamics in supercooled liquid and glassy states of a 2D monatomic system with a double-well Lennard-Jones-Gauss (LJG) interaction potential, we find a new scenario of dynamical heterogeneity. Atoms with the same or very close mobility have a tendency to aggregate into clusters. The number of atoms with high mobility (and size of their clusters) increases with decreasing temperature passing over a maximum before decreasing down to zero. Position of the peak moves toward a lower temperature if mobility of atoms in clusters is lower together with an enhancement of height of the peak. In contrast, the number of atoms with very low mobility or solidlike atoms (and size of their clusters) has a tendency to increase with decreasing temperature and then it suddenly increases in the vicinity of the glass transition temperature leading to the formation of a glassy state. A sudden increase in the number of strongly correlated solidlike atoms in the vicinity of a glass transition temperature (T-g) may be an origin of a drastical increase in viscosity of the glass-forming systems approaching the glass transition. In fact, we find that the diffusion coefficient decays exponentially with a fraction of solidlike atoms exhibiting a sudden decrease in the vicinity of the glass transition region.