We report observation of the disappearance and recreation of the rigid, or constrained, amorphous phase by sequential thermal annealing. Modulated differential scanning calorimetry (m.d.s.c.) is used to study the glass transition and lower melting endotherm after annealing. Cold crystallization at a temperature T-cc just above T-g creates an initial large fraction of rigid amorphous phase (RAP). Brief rapid annealing to a higher temperature causes the constrained amorphous phase almost to disappear completely, a result that has never been reported before. Subsequent reannealing at the original lower temperature T-cc restores RAP to its original value. At the same time that RAP is being removed, the glass transition temperature decreases; when RAP is restored, T-g increases once again. The crystal fraction remains unaffected by the annealing sequence. Results indicate that the location of the RAP is within the amorphous phase, rather than in a separate location away from the liquid-like amorphous phase.