The turbulent thermal plume developing in stably stratified air above the square heated plate on a broad and horizontal surface is computed by DNS, and is elucidated. (1) At the weakly stratified ambient, turbulence is enhanced near the plate center due to both the high speed in the flow near the plate surface toward the heated plate center and the violent oscillation in the temperature plume bottom. (2) Whether turbulence exists or not near the plate center leads to different mechanisms of the turbulence suppression. (a) At the weakly and ordinarily stratified ambient, turbulence exists near the plate center, and is suppressed, i.e. the reverse transition and relaminarization, due to the flow energy consuming by both the upward flow and the brake effect in the negative buoyant region. (b) At the strongly stratified ambient, turbulence does not exist near the plate center, and is suppressed due to laminarization in the whole region of the plume. (3) The reverse transition and relaminarization occur in the unstable region with the negative buoyancy, where the large scale fluctuation occurs, and the velocity and temperature time-records have large fluctuations, and differ each other.