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By means of the isoconfigurational method, we calculate the change in the propensity for motion that the structure of a glass-forming system experiences during its relaxation dynamics. The relaxation of such a system has been demonstrated to evolve by means of rapid crossings between metabasins of its potential energy surface a metabasin being a group of mutually similar, closely related structures which differ markedly from other metabasins, as collectively relaxing units related structures which differ markedly from other metabasins, as collectively relaxing units a metabasin being a group of mutually similar, closely related structures which differ markedly from other metabasins, as collectively relaxing units d-clusters take place. We now show that the spatial distribution of propensity in the system does not change significantly until one of these d-clusters takes place. However, the occurrence of a not change significantly until one of these d-clusters takes place. However, the occurrence of a d-clusters take place. We now show that the spatial distribution of propensity in the system does not change significantly until one of these d-clusters takes place. However, the occurrence of ad-clusters takes place. However, the occurrence of a d-cluster clearly decorrelates the propensity of the particles, thus ending up with the dynamical influence of the structural features proper of the local metabasin. We also show an important match between particles that participate in d-clusters and that which show high changes in their propensity. propensity. influence of the structural features proper of the local metabasin. We also show an important match between particles that participate in d-clusters and that which show high changes in their propensity. propensity. -cluster clearly decorrelates the propensity of the particles, thus ending up with the dynamical influence of the structural features proper of the local metabasin. We also show an important match between particles that participate in d-clusters and that which show high changes in their propensity. propensity. d-clusters and that which show high changes in their propensity.