A sorting outlet module for a postal sorting machine, provided with a bay for receiving a storage tray for storing mailpieces, and, inside the bay, is provided with a support for supporting the storage tray in the manner of a drawer. The support is mounted to move in translation in a longitudinal direction between a storage position in which the tray on the support is retracted inside the bay and a transfer position in which the tray on the support is out of the bay. The support is also provided with pivot and alignment means for pivoting and aligning the tray, which means are arranged in such a manner that pivoting the tray through 90° on the support relative to the longitudinal direction causes one end of tray to be aligned with one side of the bay while also maintaining the tray as close as possible to the bay.