An assembly is provided for freezing a plurality of conditioning tubes each filled with a predetermined volume of biological substance, in which each of the tubes is driven in rotation in a flow of cooling agent, the assembly including a cooling enclosure configured in order to be passed through by the flow of cooling agent and a conditioning unit which is removable and placed in the enclosure； the unit is provided with a greater capacity than the plurality of tubes in order to directly receive this plurality of the tubes, the enclosure is fixed and the assembly includes a unit for driving the conditioning unit in rotation, which unit for driving in rotation is provided with a connection interface on which the removable conditioning unit is placed.
